title: The Wizard of Oz (1939 film)

text: In a 2009 retrospective article about the film, "San Francisco Chronicle" film critic and author Mick LaSalle declared:


title: The Wizard of Oz (1939 film)

text: “...the entire Munchkinland sequence, from Dorothy's arrival in Oz to her departure on the yellow brick road, has to be one of the greatest in cinema history – a masterpiece of set design, costuming, choreography, music, lyrics, storytelling, and sheer imagination."


title: The Wizard of Oz (1939 film)

text: On the film review aggregator site Rotten Tomatoes, "The Wizard of Oz" has a 98% rating based on 160 reviews, with an average score of 9.5/10. Its critical consensus reads, "An absolute masterpiece whose groundbreaking visuals and deft storytelling are still every bit as resonant, "The Wizard of Oz" is a must-see film for young and old." At Metacritic, which assigns a normalized rating to reviews, the film received a score of 92 out of 100, based on 30 reviews, indicating "universal acclaim".


title: The Wizard of Oz (1939 film)

text: The American Film Institute (AFI) has compiled various lists which include this film or its elements.


title: The Wizard of Oz (1939 film)

text: An official 1972 sequel, the animated "Journey Back to Oz", featuring the voice of Judy Garland's daughter Liza Minnelli was produced to commemorate the original film's 35th anniversary.


title: The Wizard of Oz (1939 film)

text: In 1975, a comic book adaptation of the film titled "MGM's Marvelous Wizard of Oz" was released. It was the first co-production between DC Comics and Marvel Comics. Marvel planned a series of sequels based on the subsequent novels. The first, "The Marvelous Land of Oz", was published later that year. The next, "The Marvelous Ozma of Oz" was expected to be released the following year but never came to be.


title: The Wizard of Oz (1939 film)

text: In 1985, Walt Disney Productions released the live-action fantasy film "Return to Oz", starring Fairuza Balk in her film debut as a young Dorothy Gale and based on "The Marvelous Land of Oz" (1904) and "Ozma of Oz" (1907). With a darker story, it fared poorly with critics unfamiliar with the "Oz" books and was not successful at the box office, although it has since become a popular cult film, with many considering it a more loyal and faithful adaptation of what L. Frank Baum envisioned.


title: The Wizard of Oz (1939 film)

text: The Broadway musical "Wicked" premiered in 2003, and is based on the film and original novel. It has since gone on to become the second-highest grossing Broadway musical of all time, and won three Tony Awards, seven Drama Desk Awards, and a Grammy Award. A film adaptation of the musical, directed by Jon M. Chu, has been in development at Universal Pictures since 2004.


title: The Wizard of Oz (1939 film)

text: Andrew Lloyd Webber and Tim Rice produced a stage musical of the same name, which opened in 2011 at the West Ends London Palladium.


title: The Wizard of Oz (1939 film)

text: An animated film called "Tom and Jerry and the Wizard of Oz" was released in 2011 by Warner Home Video, incorporating Tom and Jerry into the story as Dorothy's "protectors". A sequel titled "" was released on DVD on June 21, 2016.


title: The Wizard of Oz (1939 film)

text: In 2013, Walt Disney Pictures released a "spiritual prequel" titled "Oz the Great and Powerful". It was directed by Sam Raimi and starred James Franco, Mila Kunis, Rachel Weisz and Michelle Williams. It was the second film based on Baum's "Oz" series to be produced by Disney, after "Return to Oz". It was a commercial success but received a mixed reception from critics.


title: The Wizard of Oz (1939 film)

text: In 2014, independent film company Clarius Entertainment released a big-budget animated musical film, "", which follows Dorothy's second trip to Oz. The film fared poorly at the box office and was received negatively by critics, largely for its plot and unmemorable musical numbers.


title: The Wizard of Oz (1939 film)

text: In February 2021, New Line Cinema, Temple Hill Entertainment and "Wicked" producer Marc Platt announced that a new film version of the original book is in the works with "Watchmen"'s Nicole Kassell slated to direct the reimagining, which will have the option to include elements from the 1939 film. In August 2022 it was announced that Kenya Barris would write and direct a modern remake.


title: The Wizard of Oz (1939 film)

text: According to the US Library of Congress exhibition "The Wizard of Oz: an American Fairy Tale" (2010):


title: The Wizard of Oz (1939 film)

text: "The Wonderful Wizard of Oz" is America's greatest and best-loved home-grown fairytale. The first totally American fantasy for children, it is one of the most-read children's books ... Despite its many particularly American attributes, including a wizard from Omaha, [the 1939 film adaptation] has universal appeal... Because of its many television showings between 1956 and 1974, it has been seen by more viewers than any other movie”.


title: The Wizard of Oz (1939 film)

text: In 1977, Aljean Harmetz wrote "The Making of The Wizard of Oz", a detailed description of the creation of the film based on interviews and research; it was updated in 1989.


title: The Wizard of Oz (1939 film)

text: Because of their iconic stature, the ruby slippers worn by Judy Garland in the film are now among the most treasured and valuable film memorabilia in movie history. Dorothy actually wore Silver Shoes in the book series, but the color was changed to ruby to take advantage of the new Technicolor process. Adrian, MGM's chief costume designer, was responsible for the final design. Five known pairs of the slippers exist. Another, differently styled pair, not used in the film, was sold at auction by actress Debbie Reynolds for $510,000 (not including the buyer's premium) in June 2011.


title: The Wizard of Oz (1939 film)

text: In July 2021, Catholic University of America reported that a dress worn by Dorothy, believed to have been given to Rev. Gilbert Hartke by Mercedes McCambridge as a gift in 1973, was found in the university's Hartke Building after being missing for many years. The university said an expert on the movie's memorabilia at the Smithsonian's National Museum of American History said five other dresses apparently worn by Judy Garland were "probably authentic". The dress found at the university had characteristics shared by the other five, including a "secret pocket" for Dorothy's handkerchief, and Garland's name written in a specific style. The university said the dress would be stored in Special Collections.


title: The Wizard of Oz (1939 film)

text: Another of the dresses sold at auction in 2015 for nearly $1.6 million. Many other costumes have fetched six-figure prices as memorabilia. See List of film memorabilia.


title: The Wizard of Oz (1939 film)

text: "The Wizard of Oz" has a presence at the Disney Parks and Resorts. The film had its own scene at The Great Movie Ride at Disney Hollywood Studios at Walt Disney World Resort, and is also represented in miniature at Disneyland and at Disneyland Paris as part of the Storybook Land Canal Boats attraction in Fantasyland.


title: Fairchild Republic A-10 Thunderbolt II

text: The Fairchild Republic A-10 Thunderbolt II is a single-seat, twin-turbofan, straight-wing, subsonic attack aircraft developed by Fairchild Republic for the United States Air Force (USAF). In service since 1976, it is named for the Republic P-47 Thunderbolt, a World War II-era fighter-bomber effective at attacking ground targets, but commonly referred to as the "Warthog" or "Hog". The A-10 was designed to provide close air support (CAS) to friendly ground troops by attacking armored vehicles, tanks, and other enemy ground forces; it is the only production-built aircraft designed solely for CAS to have served with the U.S. Air Force. Its secondary mission is to direct other aircraft in attacks on ground targets, a role called forward air controller-airborne; aircraft used primarily in this role are designated OA-10.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 was intended to improve on the performance and firepower of the Douglas A-1 Skyraider. Its airframe was designed for durability, with measures such as of titanium armor to protect the cockpit and aircraft systems, enabling it to absorb damage and continue flying. Its ability to take off and land from relatively short runways permits operation from airstrips close to the front lines, and its simple design enables maintenance with minimal facilities.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 served in the Gulf War (Operation Desert Storm), the American–led intervention against Iraq's invasion of Kuwait, where the aircraft distinguished itself. The A-10 also participated in other conflicts such as in Grenada, the Balkans, Afghanistan, Iraq, and against the Islamic State in the Middle East.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10A single-seat variant was the only version produced, though one pre-production airframe was modified into the YA-10B twin-seat prototype to test an all-weather night-capable version. In 2005, a program was started to upgrade the remaining A-10A aircraft to the A-10C configuration, with modern avionics for use with precision weaponry. The U.S. Air Force had stated the Lockheed Martin F-35 Lightning II would replace the A-10 as it entered service, but this remains highly contentious within the USAF and in political circles. With a variety of upgrades and wing replacements, the A-10's service life can be extended to 2040; the service has no planned retirement date .


title: Fairchild Republic A-10 Thunderbolt II

text: The development of conventionally armed attack aircraft in the United States stagnated after World War II, as design efforts for tactical aircraft focused on the delivery of nuclear weapons using high-speed designs like the McDonnell F-101 Voodoo and Republic F-105 Thunderchief. As the U.S. military entered the Vietnam War, its main ground-attack aircraft was the Korean War-era Douglas A-1 Skyraider. A capable aircraft for its era, with a relatively large payload and long loiter time, the propeller-driven design was relatively slow and vulnerable to ground fire. The U.S. Air Force and Navy lost 266 A-1s in action in Vietnam, largely from small-arms fire. The A-1 Skyraider also had poor firepower.


title: Fairchild Republic A-10 Thunderbolt II

text: The lack of modern conventional attack capability prompted calls for a specialized attack aircraft. On 7 June 1961, the Secretary of Defense Robert McNamara ordered the USAF to develop two tactical aircraft, one for the long-range strike and interdictor role, and the other focusing on the fighter-bomber mission. The former was the Tactical Fighter Experimental (TFX) intended to be common design for the USAF and the US Navy, which emerged as the General Dynamics F-111 Aardvark, while the second was filled by a version of the U.S. Navy's McDonnell Douglas F-4 Phantom II. While the Phantom went on to be one of the most successful fighter designs of the 1960s and proved to be a capable fighter-bomber, its lack of loiter time was a major problem, and to a lesser extent, its poor low-speed performance. It was also expensive to buy and operate, with a flyaway cost of $2 million in FY1965 ($ million today), and operational costs over $900 per hour ($ per hour today).


title: Fairchild Republic A-10 Thunderbolt II

text: After a broad review of its tactical force structure, the U.S. Air Force decided to adopt a low-cost aircraft to supplement the F-4 and F-111. It first focused on the Northrop F-5, which had air-to-air capability. A 1965 cost-effectiveness study shifted the focus from the F-5 to the less expensive A-7D variant of the LTV A-7 Corsair II, and a contract was awarded. However, this aircraft doubled in cost with demands for an upgraded engine and new avionics.


title: Fairchild Republic A-10 Thunderbolt II

text: During this period, the United States Army had been introducing the Bell UH-1 Iroquois into service. First used in its intended role as a transport, it was soon modified in the field to carry more machine guns in what became known as the helicopter gunship role. This proved effective against the lightly armed enemy, and new gun and rocket pods were added. Soon the Bell AH-1 Cobra was introduced. This was an attack helicopter armed with long-range BGM-71 TOW missiles able to destroy tanks from outside the range of defensive fire. The helicopter was effective and prompted the U.S. military to change its defensive strategy in Europe into blunting any Warsaw Pact advance with anti-tank helicopters instead of the tactical nuclear weapons that had been the basis for NATO's battle plans since the 1950s.


title: Fairchild Republic A-10 Thunderbolt II

text: The Cobra was a quickly-made helicopter based on the UH-1 Iroquois and was introduced in the mid-1960s as an interim design until the U.S. Army "Advanced Aerial Fire Support System" program delivered. The Army selected the Lockheed AH-56 Cheyenne, a much more capable attack aircraft with greater speed for initial production. These developments worried the USAF, which saw the anti-tank helicopter overtaking its nuclear-armed tactical aircraft as the primary anti-armor force in Europe. A 1966 Air Force study of existing close air support (CAS) capabilities revealed gaps in the escort and fire suppression roles, which the Cheyenne could fill. The study concluded that the service should acquire a simple, inexpensive, dedicated CAS aircraft at least as capable as the A-1, and that it should develop doctrine, tactics, and procedures for such aircraft to accomplish the missions for which the attack helicopters were provided.


title: Fairchild Republic A-10 Thunderbolt II

text: On 8 September 1966, General John P. McConnell, Chief of Staff of the USAF, ordered that a specialized CAS aircraft be designed, developed, and obtained. On 22 December, a Requirements Action Directive was issued for the A-X CAS airplane, and the Attack Experimental (A-X) program office was formed. On 6 March 1967, the Air Force released a request for information to 21 defense contractors for the A-X.


title: Fairchild Republic A-10 Thunderbolt II

text: In May 1970, the USAF issued a modified, more detailed request for proposals for the aircraft. The threat of Soviet armored forces and all-weather attack operations had become more serious. The requirements now included that the aircraft would be designed specifically for the 30 mm rotary cannon. The RFP also specified a maximum speed of , takeoff distance of , external load of , mission radius, and a unit cost of US$1.4 million ($ million today). The A-X would be the first USAF aircraft designed exclusively for close air support. During this time, a separate RFP was released for A-X's 30 mm cannon with requirements for a high rate of fire (4,000 round per minute) and a high muzzle velocity. Six companies submitted aircraft proposals, with Northrop and Fairchild Republic selected to build prototypes: the YA-9A and YA-10A, respectively. General Electric and Philco-Ford were selected to build and test GAU-8 cannon prototypes.


title: Fairchild Republic A-10 Thunderbolt II

text: Two YA-10 prototypes were built in the Republic factory in Farmingdale, New York, and first flown on 10 May 1972 by pilot Howard "Sam" Nelson. Production A-10s were built by Fairchild in Hagerstown, Maryland. After trials and a fly-off against the YA-9, on 18 January 1973, the USAF announced the YA-10's selection for production. General Electric was selected to build the GAU-8 cannon in June 1973. The YA-10 had an additional fly-off in 1974 against the Ling-Temco-Vought A-7D Corsair II, the principal USAF attack aircraft at the time, to prove the need for a new attack aircraft. The first production A-10 flew in October 1975, and deliveries commenced in March 1976.


title: Fairchild Republic A-10 Thunderbolt II

text: One experimental two-seat A-10 Night Adverse Weather (N/AW) version was built by converting an A-10A. The N/AW was developed by Fairchild from the first Demonstration Testing and Evaluation (DT&E) A-10 for consideration by the USAF. It included a second seat for a weapon systems officer responsible for electronic countermeasures (ECM), navigation and target acquisition. The N/AW version did not interest the USAF or export customers. The two-seat trainer version was ordered by the Air Force in 1981, but funding was canceled by U.S. Congress and the trainer was not produced. The only two-seat A-10 resides at Edwards Air Force Base's Flight Test Center Museum.


title: Fairchild Republic A-10 Thunderbolt II

text: On 10 February 1976, Deputy Secretary of Defense Bill Clements authorized full-rate production, with the first A-10 being accepted by the Air Force Tactical Air Command on 30 March 1976. Production continued and reached a peak rate of 13 aircraft per month. By 1984, 715 airplanes, including two prototypes and six development aircraft, had been delivered.


title: Fairchild Republic A-10 Thunderbolt II

text: When A-10 full-rate production was first authorized the aircraft's planned service life was 6,000 hours. A small reinforcement to the design was quickly adopted when the A-10 failed initial fatigue testing at 80% of testing; with the fix, the A-10 passed the fatigue tests. 8,000-flight-hour service lives were becoming common at the time, so fatigue testing of the A-10 continued with a new 8,000-hour target. This new target quickly discovered serious cracks at Wing Station 23 (WS23) where the outboard portions of the wings are joined to the fuselage. The first production change was to add cold working at WS23 to address this problem. Soon after, the Air Force determined that the real-world A-10 fleet fatigue was more harsh than estimated, forcing them to change their fatigue testing and introduce "spectrum 3" equivalent flight-hour testing.


title: Fairchild Republic A-10 Thunderbolt II

text: Spectrum 3 fatigue testing started in 1979. This round of testing quickly determined that more drastic reinforcement would be needed. The second change in production, starting with aircraft No. 442, was to increase the thickness of the lower skin on the outer wing panels. A tech order was issued to retrofit the "thick skin" to the whole fleet, but the tech order was rescinded after roughly 242 planes, leaving about 200 planes with the original "thin skin". Starting with aircraft No. 530, cold working at WS0 was performed, and this retrofit was performed on earlier aircraft. A fourth, even more drastic change was initiated with aircraft No. 582, again to address the problems discovered with spectrum 3 testing. This change increased the thickness of the lower skin on the center wing panel, but it required modifications to the lower spar caps to accommodate the thicker skin. The Air Force determined that it was not economically feasible to retrofit earlier planes with this modification.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 has received many upgrades since entering service. In 1978, the A-10 received the Pave Penny laser receiver pod, which receives reflected laser radiation from laser designators to allow the aircraft to deliver laser guided munitions. The Pave Penny pod is carried on a pylon mounted below the right side of the cockpit and has a clear view of the ground. In 1980, the A-10 began receiving an inertial navigation system.


title: Fairchild Republic A-10 Thunderbolt II

text: In the early 1990s, the A-10 began to receive the Low-Altitude Safety and Targeting Enhancement (LASTE) upgrade, which provided computerized weapon-aiming equipment, an autopilot, and a ground-collision warning system. In 1999, aircraft began receiving Global Positioning System navigation systems and a multi-function display. The LASTE system was upgraded with an Integrated Flight & Fire Control Computer (IFFCC).


title: Fairchild Republic A-10 Thunderbolt II

text: Proposed further upgrades included integrated combat search and rescue locator systems and improved early warning and anti-jam self-protection systems, and the Air Force recognized that the A-10's engine power was sub-optimal and had been planning to replace them with more powerful engines since at least 2001 at an estimated cost of $2 billion.


title: Fairchild Republic A-10 Thunderbolt II

text: In 1987, Grumman Aerospace took over support for the A-10 program. In 1993, Grumman updated the damage tolerance assessment and Force Structural Maintenance Plan and Damage Threat Assessment. Over the next few years, problems with wing structure fatigue, first noticed in production years earlier, began to come to the fore. The process of implementing the maintenance plan was greatly delayed by the base realignment and closure commission (BRAC), which led to 80% of the original workforce being let go.


title: Fairchild Republic A-10 Thunderbolt II

text: During inspections in 1995 and 1996, cracks at the WS23 location were found on many aircraft, most of them in line with updated predictions from 1993. However, two of these were classified as "near-critical" size, well beyond predictions. In August 1998, Grumman produced a new plan to address these issues and increase life span to 16,000 hours. This resulted in the "HOG UP" program, which commenced in 1999. Over time, additional aspects were added to HOG UP, including new fuel bladders, changes to the flight control system, and inspections of the engine nacelles. In 2001, the cracks were reclassified as "critical", which meant they were considered repairs and not upgrades, which allowed bypassing normal acquisition channels for more rapid implementation.


title: Fairchild Republic A-10 Thunderbolt II

text: An independent review of the HOG UP program at this point concluded that the data on which the wing upgrade relied could no longer be trusted. This independent review was presented in September 2003. Shortly thereafter, fatigue testing on a test wing failed prematurely and also mounting problems with wings failing in-service inspections at an increasing rate became apparent. The Air Force estimated that they would run out of wings by 2011. Of the plans explored, replacing the wings with new ones was the least expensive, with an initial cost of $741 million, and a total cost of $1.72 billion over the life of the program.


title: Fairchild Republic A-10 Thunderbolt II

text: In 2005, a business case was developed with three options to extend the life of the fleet. The first two options involved expanding the service life extension program (SLEP) at a cost of $4.6 billion and $3.16 billion, respectively. The third option, worth $1.72 billion, was to build 242 new wings and avoid the cost of expanding the SLEP. In 2006, option 3 was chosen and Boeing won the contract. The base contract is for 117 wings with options for 125 additional wings. In 2013, the Air Force exercised a portion of the option to add 56 wings, putting 173 wings on order with options remaining for 69 additional wings. In November 2011, two A-10s flew with the new wings fitted. The new wings improved mission readiness, decreased maintenance costs, and allowed the A-10 to be operated up to 2035 if necessary. The re-winging effort was organized under the Thick-skin Urgent Spares Kitting (TUSK) Program.


title: Fairchild Republic A-10 Thunderbolt II

text: In 2014, as part of plans to retire the A-10, the USAF considered halting the wing replacement program to save an additional $500 million; however, by May 2015 the re-winging program was too far into the contract to be financially efficient to cancel. Boeing stated in February 2016 that the A-10 fleet with the new TUSK wings could operate to 2040.


title: Fairchild Republic A-10 Thunderbolt II

text: In 2005, the entire fleet of 356 A-10 and OA-10 aircraft began receiving the Precision Engagement upgrades including an improved fire control system (FCS), electronic countermeasures (ECM), and smart bomb targeting. The aircraft receiving this upgrade were redesignated A-10C. The Government Accountability Office in 2007 estimated the cost of upgrading, refurbishing, and service life extension plans for the A-10 force to total $2.25 billion through 2013. In July 2010, the USAF issued Raytheon a contract to integrate a Helmet Mounted Integrated Targeting (HMIT) system into the A-10C. The Air Force Materiel Command's Ogden Air Logistics Center at Hill AFB, Utah completed work on its 100th A-10 precision engagement upgrade in January 2008. The final aircraft was upgraded to A-10C configuration in June 2011. The aircraft also received all-weather combat capability, and a Hand-on-Throttle-and-Stick configuration mixing the F-16's flight stick with the F-15's throttle. Other changes included two multifunction displays, a modern communications suite including a Link-16 radio and SATCOM. The LASTE system was replaced with the integrated flight and fire control computer (IFFCC) included in the PE upgrade.


title: Fairchild Republic A-10 Thunderbolt II

text: Throughout its life, the platform's software has been upgraded several times, and although these upgrades were due to be stopped as part of plans to retire the A-10 in February 2014, Secretary of the Air Force Deborah Lee James ordered that the latest upgrade, designated Suite 8, continue in response to Congressional pressure. Suite 8 software includes IFF Mode 5, which modernizes the ability to identify the A-10 to friendly units. Additionally, the Pave Penny pods and pylons are being removed as their receive-only capability has been replaced by the AN/AAQ-28(V)4 LITENING AT targeting pods or Sniper XR targeting pod, which both have laser designators and laser rangefinders.


title: Fairchild Republic A-10 Thunderbolt II

text: In 2012, Air Combat Command requested the testing of a external fuel tank which would extend the A-10's loitering time by 45–60 minutes; flight testing of such a tank had been conducted in 1997 but did not involve combat evaluation. Over 30 flight tests were conducted by the 40th Flight Test Squadron to gather data on the aircraft's handling characteristics and performance across different load configurations. It was reported that the tank slightly reduced stability in the yaw axis, but there was no decrease in aircraft tracking performance.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 has a cantilever low-wing monoplane wing with a wide chord. The aircraft has superior maneuverability at low speeds and altitude because of its large wing area, high wing aspect ratio, and large ailerons. The wing also allows short takeoffs and landings, permitting operations from primitive forward airfields near front lines. The aircraft can loiter for extended periods and operate under ceilings with visibility. It typically flies at a relatively low speed of , which makes it a better platform for the ground-attack role than fast fighter-bombers, which often have difficulty targeting small, slow-moving targets.


title: Fairchild Republic A-10 Thunderbolt II

text: The leading edge of the wing has a honeycomb structure panel construction, providing strength with minimal weight; similar panels cover the flap shrouds, elevators, rudders and sections of the fins. The skin panels are integral with the stringers and are fabricated using computer-controlled machining, reducing production time and cost. Combat experience has shown that this type of panel is more resistant to damage. The skin is not load-bearing, so damaged skin sections can be easily replaced in the field, with makeshift materials if necessary. The ailerons are at the far ends of the wings for greater rolling moment and have two distinguishing features: The ailerons are larger than is typical, almost 50 percent of the wingspan, providing improved control even at slow speeds; the aileron is also split, making it a deceleron.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 is designed to be refueled, rearmed, and serviced with minimal equipment. Its simple design enables maintenance at forward bases with limited facilities. An unusual feature is that many of the aircraft's parts are interchangeable between the left and right sides, including the engines, main landing gear, and vertical stabilizers. The sturdy landing gear, low-pressure tires and large, straight wings allow operation from short rough strips even with a heavy aircraft ordnance load, allowing the aircraft to operate from damaged airbases, flying from taxiways, or even straight roadway sections.


title: Fairchild Republic A-10 Thunderbolt II

text: The front landing gear is offset to the aircraft's right to allow placement of the 30 mm cannon with its firing barrel along the centerline of the aircraft. During ground taxi, the offset front landing gear causes the A-10 to have dissimilar turning radii; turning to the right on the ground takes less distance than turning left. The wheels of the main landing gear partially protrude from their nacelles when retracted, making gear-up belly landings easier to control and less damaging. All landing gears retract forward; if hydraulic power is lost, a combination of gravity and aerodynamic drag can lower and lock the gear in place.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 is battle-hardened to an exceptional degree, being able to survive direct hits from armor-piercing and high-explosive projectiles up to 23 mm. It has double-redundant hydraulic flight systems, and a mechanical system as a backup if hydraulics are lost. Flight without hydraulic power uses the manual reversion control system; pitch and yaw control engages automatically, roll control is pilot-selected. In manual reversion mode, the A-10 is sufficiently controllable under favorable conditions to return to base, though control forces are greater than normal. The aircraft is designed to be able to fly with one engine, half of the tail, one elevator, and half of a wing missing.


title: Fairchild Republic A-10 Thunderbolt II

text: The cockpit and parts of the flight-control systems are protected by of titanium aircraft armor, referred to as a "bathtub". The armor has been tested to withstand strikes from 23 mm cannon fire and some indirect hits from 57 mm shell fragments. It is made up of titanium plates with thicknesses varying from determined by a study of likely trajectories and deflection angles. The armor makes up almost six percent of the aircraft's empty weight. Any interior surface of the tub directly exposed to the pilot is covered by a multi-layer nylon spall shield to protect against shell fragmentation. The front windscreen and canopy are resistant to small arms fire.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10's durability was demonstrated on 7 April 2003 when Captain Kim Campbell, while flying over Baghdad during the 2003 invasion of Iraq, suffered extensive flak damage. Iraqi fire damaged one of her engines and crippled the hydraulic system, requiring the aircraft's stabilizer and flight controls to be operated via the 'manual reversion mode.' Despite this damage, Campbell flew the aircraft for nearly an hour and landed safely.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 was intended to fly from forward air bases and semi-prepared runways where foreign object damage to an aircraft's engines is normally a high risk. The unusual location of the General Electric TF34-GE-100 turbofan engines decreases ingestion risk and also allows the engines to run while the aircraft is serviced and rearmed by ground crews, reducing turn-around time. The wings are also mounted closer to the ground, simplifying servicing and rearming operations. The heavy engines require strong supports: four bolts connect the engine pylons to the airframe. The engines' high 6:1 bypass ratio contributes to a relatively small infrared signature, and their position directs exhaust over the tailplanes further shielding it from detection by infrared homing surface-to-air missiles. The engines' exhaust nozzles are angled nine degrees below horizontal to cancel out the nose-down pitching moment that would otherwise be generated from being mounted above the aircraft's center of gravity and avoid the need to trim the control surfaces to prevent pitching.


title: Fairchild Republic A-10 Thunderbolt II

text: To reduce the likelihood of damage to the A-10's fuel system, all four fuel tanks are located near the aircraft's center and are separated from the fuselage; projectiles would need to penetrate the aircraft's skin before reaching a tank's outer skin. Compromised fuel transfer lines self-seal; if damage exceeds a tank's self-sealing capabilities, check valves prevent fuel flowing into a compromised tank. Most fuel system components are inside the tanks so that fuel will not be lost due to component failure. The refueling system is also purged after use. Reticulated polyurethane foam lines both the inner and outer sides of the fuel tanks, retaining debris and restricting fuel spillage in the event of damage. The engines are shielded from the rest of the airframe by firewalls and fire extinguishing equipment. In the event of all four main tanks being lost, two self-sealing sump tanks contain fuel for 230 miles (370 km) of flight.


title: Fairchild Republic A-10 Thunderbolt II

text: Since the A-10 operates very close to enemy positions, where it is an easy target for man-portable air-defense system (MANPADS), surface-to-air missiles (SAMs), and enemy aircraft, it carries both flares and chaff cartridges.


title: Fairchild Republic A-10 Thunderbolt II

text: Although the A-10 can carry a considerable amount of munitions, its primary built-in weapon is the 30×173 mm GAU-8/A Avenger autocannon. One of the most powerful aircraft cannons ever flown, it fires large depleted uranium armor-piercing shells. The GAU-8 is a hydraulically driven seven-barrel rotary cannon designed specifically for the anti-tank role with a high rate of fire. The cannon's original design could be switched by the pilot to 2,100 or 4,200 rounds per minute; this was later changed to a fixed rate of 3,900 rounds per minute. The cannon takes about half a second to reach top speed, so 50 rounds are fired during the first second, 65 or 70 rounds per second thereafter. The gun is accurate enough to place 80 percent of its shots within a 40-foot (12.4 m) diameter circle from 4,000 feet (1,220 m) while in flight. The GAU-8 is optimized for a slant range of with the A-10 in a 30-degree dive.


title: Fairchild Republic A-10 Thunderbolt II

text: The fuselage of the aircraft is built around the cannon. The GAU-8/A is mounted slightly to the port side; the barrel in the firing location is on the starboard side so it is aligned with the aircraft's centerline. The gun's 5-foot, 11.5-inch (1.816 m) ammunition drum can hold up to 1,350 rounds of 30 mm ammunition, but generally holds 1,174 rounds. To protect the GAU-8/A rounds from enemy fire, armor plates of differing thicknesses between the aircraft skin and the drum are designed to detonate incoming shells.


title: Fairchild Republic A-10 Thunderbolt II

text: The AGM-65 Maverick air-to-surface missile is a commonly used munition for the A-10, targeted via electro-optical (TV-guided) or infrared. The Maverick allows target engagement at much greater ranges than the cannon, and thus less risk from anti-aircraft systems. During Desert Storm, in the absence of dedicated forward-looking infrared (FLIR) cameras for night vision, the Maverick's infrared camera was used for night missions as a "poor man's FLIR". Other weapons include cluster bombs and Hydra 70 rocket pods. The A-10 is equipped to carry GPS- and laser-guided bombs, such as the GBU-39 Small Diameter Bomb, Paveway series bombs, Joint Direct Attack Munitions (JDAM), Wind Corrected Munitions Dispenser and AGM-154 Joint Standoff Weapon glide bombs. A-10s usually fly with an ALQ-131 Electronic countermeasures (ECM) pod under one wing and two AIM-9 Sidewinder air-to-air missiles for self-defense under the other wing.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 Precision Engagement Modification Program from 2006 to 2010 updated all A-10 and OA-10 aircraft in the fleet to the A-10C standard with a new flight computer, new glass cockpit displays and controls, two new color displays with moving map function, and an integrated digital stores management system.


title: Fairchild Republic A-10 Thunderbolt II

text: Since then, the A-10 Common Fleet Initiative has led to further improvements: a new wing design, a new data link, the ability to employ smart weapons such as the Joint Direct Attack Munition (JDAM) and Wind Corrected Munitions Dispenser, as well as the newer GBU-39 Small Diameter Bomb, and the ability to carry an integrated targeting pod such as the Northrop Grumman Litening or the Lockheed Martin Sniper Advanced Targeting Pod (ATP). Also included is the Remotely Operated Video Enhanced Receiver (ROVER) to provide sensor data to personnel on the ground. The A-10C has a Missile Warning System (MWS), which alerts the pilot to whenever there is a missile launch, friendly or non-friendly. The A-10C can also carry a ALQ-184 ECM Pod, which works with the MWS to detect a missile launch, figure out what kind of vehicle is launching the missile or flak (i.e.: SAM, aircraft, flak, MANPAD, etc.) and then jams it with confidential emitting, and selects a countermeasure program that the pilot has pre-set, that when turned on, will automatically dispense flare and chaff at pre-set intervals and amounts.


title: Fairchild Republic A-10 Thunderbolt II

text: Since the A-10 flies low to the ground and at subsonic speed, aircraft camouflage is important to make the aircraft more difficult to see. Many different types of paint schemes have been tried. These have included a "peanut scheme" of sand, yellow and field drab; black and white colors for winter operations and a tan, green and brown mixed pattern. Many A-10s also featured a false canopy painted in dark gray on the underside of the aircraft, just behind the gun. This form of automimicry is an attempt to confuse the enemy as to aircraft attitude and maneuver direction. Many A-10s feature nose art, such as shark mouth or warthog head features.


title: Fairchild Republic A-10 Thunderbolt II

text: The two most common markings applied to the A-10 have been the European I woodland camouflage scheme and a two-tone gray scheme. The European woodland scheme was designed to minimize visibility from above, as the threat from hostile fighter aircraft was felt to outweigh that from ground-fire. It uses dark green, medium green and dark gray to blend in with the typical European forest terrain and was used from the 1980s to the early 1990s. Following the end of the Cold War, and based on experience during the 1991 Gulf War, the air-to-air threat was no longer seen to be as important as that from ground fire, and a new color scheme known as "Compass Ghost" was chosen to minimize visibility from below. This two-tone gray scheme has darker gray color on top, with the lighter gray on the underside of the aircraft, and started to be applied from the early 1990s.


title: Fairchild Republic A-10 Thunderbolt II

text: The first unit to receive the A-10 Thunderbolt II was the 355th Tactical Training Wing, based at Davis-Monthan Air Force Base, Arizona, in March 1976. The first unit to achieve full combat readiness was the 354th Tactical Fighter Wing at Myrtle Beach Air Force Base, South Carolina, in October 1977. Deployments of A-10As followed at bases both at home and abroad, including England AFB, Louisiana; Eielson AFB, Alaska; Osan Air Base, South Korea; and RAF Bentwaters/RAF Woodbridge, England. The 81st TFW of RAF Bentwaters/RAF Woodbridge operated rotating detachments of A-10s at four bases in Germany known as Forward Operating Locations (FOLs): Leipheim, Sembach Air Base, Nörvenich Air Base, and RAF Ahlhorn.


title: Fairchild Republic A-10 Thunderbolt II

text: A-10s were initially an unwelcome addition to many in the Air Force. Most pilots switching to the A-10 did not want to because fighter pilots traditionally favored speed and appearance. In 1987, many A-10s were shifted to the forward air control (FAC) role and redesignated "OA-10". In the FAC role, the OA-10 is typically equipped with up to six pods of 2.75 inch (70 mm) Hydra rockets, usually with smoke or white phosphorus warheads used for target marking. OA-10s are physically unchanged and remain fully combat capable despite the redesignation.


title: Fairchild Republic A-10 Thunderbolt II

text: A-10s of the 23rd TFW were deployed to Bridgetown, Barbados during Operation Urgent Fury, the 1983 American Invasion of Grenada. They provided air cover for the U.S. Marine Corps landings on the island of Carriacou in late October 1983, but did not fire weapons as Marines met no resistance.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 was used in combat for the first time during the Gulf War in 1991, with 132 being deployed. A-10s shot down two Iraqi helicopters with the GAU-8 cannon. The first of these was shot down by Captain Robert Swain over Kuwait on 6 February 1991 for the A-10's first air-to-air victory. Four A-10s were shot down during the war by surface-to-air missiles and eleven A-10s were hit by anti-air artillery rounds. Another two battle-damaged A-10s and OA-10As returned to base and were written off. Some sustained additional damage in crash landings. In the beginning of the war, A-10s flew missions against the Iraqi Republican Guard, but due to heavy attrition, from the 15 February they were restricted to within 20 nautical miles (37 km) of the southern border. A-10s also flew missions hunting Iraqi Scud missiles. The A-10 had a mission capable rate of 95.7 percent, flew 8,100 sorties, and launched 90 percent of the AGM-65 Maverick missiles fired in the conflict. Shortly after the Gulf War, the Air Force abandoned the idea of replacing the A-10 with a close air support version of the F-16.<ref name="F/A-16">"A-16 Close Air Support". "F-16.net". Retrieved 5 March 2010.</ref>


title: Fairchild Republic A-10 Thunderbolt II

text: U.S. Air Force A-10 aircraft fired approximately 10,000 30 mm rounds in Bosnia and Herzegovina in 1994–95. Following the seizure of some heavy weapons by Bosnian Serbs from a warehouse in Ilidža, a series of sorties were launched to locate and destroy the captured equipment. On 5 August 1994, two A-10s located and strafed an anti-tank vehicle. Afterward, the Serbs agreed to return the remaining heavy weapons. In August 1995, NATO launched an offensive called Operation Deliberate Force. A-10s flew close air support missions, attacking Bosnian Serb artillery and positions. In late September, A-10s began flying patrols again.


title: Fairchild Republic A-10 Thunderbolt II

text: A-10s returned to the Balkan region as part of Operation Allied Force in Kosovo beginning in March 1999. In March 1999, A-10s escorted and supported search and rescue helicopters in finding a downed F-117 pilot. The A-10s were deployed to support search and rescue missions, but over time the Warthogs began to receive more ground attack missions. The A-10's first successful attack in Operation Allied Force happened on 6 April 1999; A-10s remained in action until combat ended in late June 1999.


title: Fairchild Republic A-10 Thunderbolt II

text: During the 2001 invasion of Afghanistan, A-10s did not take part in the initial stages. For the campaign against Taliban and Al Qaeda, A-10 squadrons were deployed to Pakistan and Bagram Air Base, Afghanistan, beginning in March 2002. These A-10s participated in Operation Anaconda. Afterward, A-10s remained in-country, fighting Taliban and Al Qaeda remnants.


title: Fairchild Republic A-10 Thunderbolt II

text: Operation Iraqi Freedom began on 20 March 2003. Sixty OA-10/A-10 aircraft took part in early combat there. United States Air Forces Central Command issued "Operation Iraqi Freedom: By the Numbers", a declassified report about the aerial campaign in the conflict on 30 April 2003. During that initial invasion of Iraq, A-10s had a mission capable rate of 85 percent in the war and fired 311,597 rounds of 30 mm ammunition. A single A-10 was shot down near Baghdad International Airport by Iraqi fire late in the campaign. The A-10 also flew 32 missions in which the aircraft dropped propaganda leaflets over Iraq.


title: Fairchild Republic A-10 Thunderbolt II

text: In September 2007, the A-10C with the Precision Engagement Upgrade reached initial operating capability. The A-10C first deployed to Iraq in 2007 with the 104th Fighter Squadron of the Maryland Air National Guard. The A-10C's digital avionics and communications systems have greatly reduced the time to acquire a close air support target and attack it.


title: Fairchild Republic A-10 Thunderbolt II

text: A-10s flew 32 percent of combat sorties in Operation Iraqi Freedom and Operation Enduring Freedom. The sorties ranged from 27,800 to 34,500 annually between 2009 and 2012. In the first half of 2013, they flew 11,189 sorties in Afghanistan. From the beginning of 2006 to October 2013, A-10s conducted 19 percent of CAS missions in Iraq and Afghanistan, more than the F-15E Strike Eagle and B-1B Lancer, but less than the 33 percent flown by F-16s.


title: Fairchild Republic A-10 Thunderbolt II

text: In March 2011, six A-10s were deployed as part of Operation Odyssey Dawn, the coalition intervention in Libya. They participated in attacks on Libyan ground forces there.


title: Fairchild Republic A-10 Thunderbolt II

text: The USAF 122nd Fighter Wing revealed it would deploy to the Middle East in October 2014 with 12 of the unit's 21 A-10 aircraft. Although the deployment had been planned a year in advance in a support role, the timing coincided with the ongoing Operation Inherent Resolve against ISIL militants. From mid-November, U.S. commanders began sending A-10s to hit IS targets in central and northwestern Iraq on an almost daily basis. In about two months time, A-10s flew 11 percent of all USAF sorties since the start of operations in August 2014. On 15 November 2015, two days after the ISIL attacks in Paris, A-10s and AC-130s destroyed a convoy of over 100 ISIL-operated oil tanker trucks in Syria. The attacks were part of an intensification of the U.S.-led intervention against ISIL called Operation Tidal Wave II (named after Operation Tidal Wave during World War II, a failed attempt to raid German oil fields) in an attempt to cut off oil smuggling as a source of funding for the group.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 has been involved with killing ten U.S. troops in friendly-fire over four incidents between 2001 to 2015 and 35 Afghan civilians from 2010 to 2015, more than any other U.S. military aircraft; these incidents have been assessed as "inconclusive and statistically insignificant" in terms of the warplane's capability.


title: Fairchild Republic A-10 Thunderbolt II

text: On 19 January 2018, 12 A-10s from the 303d Expeditionary Fighter Squadron were deployed to Kandahar Airfield, Afghanistan, to provide close-air support, marking the first time in more than three years A-10s had been deployed to Afghanistan.


title: Fairchild Republic A-10 Thunderbolt II

text: The future of the platform remains the subject of debate. In 2007, the USAF expected the A-10 to remain in service until 2028 and possibly later, when it would likely be replaced by the Lockheed Martin F-35 Lightning II. However, critics have said that replacing the A-10 with the F-35 would be a "giant leap backwards" given the A-10's performance and the F-35's high costs. In 2012, the Air Force considered the F-35B STOVL variant as a replacement CAS aircraft, but concluded that the aircraft could not generate sufficient sorties. In August 2013, Congress and the Air Force examined various proposals, including the F-35 and the MQ-9 Reaper unmanned aerial vehicle filling the A-10's role. Proponents state that the A-10's armor and cannon are superior to aircraft such as the F-35 for ground attack, that guided munitions other planes rely upon could be jammed, and that ground commanders frequently request A-10 support.


title: Fairchild Republic A-10 Thunderbolt II

text: In the USAF's FY 2015 budget, the service considered retiring the A-10 and other single-mission aircraft, prioritizing multi-mission aircraft; cutting a whole fleet and its infrastructure was seen as the only method for major savings. The U.S. Army had expressed interest in obtaining some A-10s should the Air Force retire them, but later stated there was "no chance" of that happening. The U.S. Air Force stated that retirement would save $3.7 billion from 2015 to 2019. The prevalence of guided munitions allows more aircraft to perform the CAS mission and reduces the requirement for specialized aircraft; since 2001 multirole aircraft and bombers have performed 80 percent of operational CAS missions. The Air Force also said that the A-10 was more vulnerable to advanced anti-aircraft defenses, but the Army replied that the A-10 had proved invaluable because of its versatile weapons loads, psychological impact, and limited logistics needs on ground support systems.


title: Fairchild Republic A-10 Thunderbolt II

text: In January 2015, USAF officials told lawmakers that it would take 15 years to fully develop a new attack aircraft to replace the A-10; that year General Herbert J. Carlisle, the head of Air Combat Command, stated that a follow-on weapon system for the A-10 may need to be developed. It planned for F-16s and F-15Es to initially take up CAS sorties, and later by the F-35A once sufficient numbers become operationally available over the next decade. In July 2015, Boeing held initial discussions on the prospects of selling retired or stored A-10s in near-flyaway condition to international customers. However, the Air Force then said that it would not permit the aircraft to be sold.


title: Fairchild Republic A-10 Thunderbolt II

text: Plans to develop a replacement aircraft were announced by the US Air Combat Command in August 2015. Early the following year, the Air Force began studying future CAS aircraft to succeed the A-10 in low-intensity "permissive conflicts" like counterterrorism and regional stability operations, admitting that the F-35 would be too expensive to operate in day-to-day roles. A wide range of platforms were under consideration, including everything from low-end AT-6 Wolverine and A-29 Super Tucano turboprops and the Textron AirLand Scorpion as more basic off-the-shelf options to more sophisticated clean-sheet attack aircraft or "AT-X" derivatives of the T-X next-generation trainer as entirely new attack platforms.


title: Fairchild Republic A-10 Thunderbolt II

text: In January 2016, the USAF was "indefinitely freezing" plans to retire the A-10 for at least several years. In addition to Congressional opposition, its use in anti-ISIS operations, deployments to Eastern Europe as a response to Russia's military intervention in Ukraine, and reevaluation of F-35 numbers necessitated its retention. In February 2016, the Air Force deferred the final retirement of the aircraft until 2022 after being replaced by F-35s on a squadron-by-squadron basis. In October 2016, the Air Force Materiel Command brought the depot maintenance line back to full capacity in preparation for re-winging the fleet. In June 2017, it was announced that the aircraft "...will now be kept in the air force’s inventory indefinitely." The 2022 Russian invasion of Ukraine spurred some American observers to push for the loaning of A-10s to Ukraine, particularly following reports of an extended, stalled Russian convoy outside Kyiv, with critics of such a proposal noting the diplomatic and tactical complications to such an approach.


title: Fairchild Republic A-10 Thunderbolt II

text: On 25 March 2010, an A-10 conducted the first flight of an aircraft with all engines powered by a biofuel blend. The flight, performed at Eglin Air Force Base, used a 1:1 blend of JP-8 and Camelina-based fuel. On 28 June 2012, the A-10 became the first aircraft to fly using a new fuel blend derived from alcohol; known as ATJ (Alcohol-to-Jet), the fuel is cellulosic-based and can be produced using wood, paper, grass, or any cellulose based material, which are fermented into alcohols before being hydro-processed into aviation fuel. ATJ is the third alternative fuel to be evaluated by the Air Force as a replacement for the petroleum-derived JP-8 fuel. Previous types were a synthetic paraffinic kerosene derived from coal and natural gas and a bio-mass fuel derived from plant-oils and animal fats known as Hydroprocessed Renewable Jet.


title: Fairchild Republic A-10 Thunderbolt II

text: In 2011, the National Science Foundation granted $11 million to modify an A-10 for weather research for CIRPAS at the U.S. Naval Postgraduate School and in collaboration with scientists from the South Dakota School of Mines & Technology (SDSM&T), replacing SDSM&T's retired North American T-28 Trojan. The A-10's armor is expected to allow it to survive the extreme meteorological conditions, such as 200 mph hailstorms, found in inclement high-altitude weather events. In 2018, this plan was found to carry too many risks associated with the costly modifications required and the program was cancelled.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 has been flown exclusively by the United States Air Force and its Air Reserve components, the Air Force Reserve Command (AFRC) and the Air National Guard (ANG). , 282 A-10C aircraft are reported as operational, divided as follows: 141 USAF, 55 AFRC, 86 ANG.


title: Fairchild Republic A-10 Thunderbolt II

text: The A-10 Thunderbolt II received its popular nickname "Warthog" from the pilots and crews of the USAF attack squadrons who flew and maintained it. The A-10 is the last of Republic's jet attack aircraft to serve with the USAF. The Republic F-84 Thunderjet was nicknamed the "Hog", F-84F Thunderstreak nicknamed "Superhog", and the Republic F-105 Thunderchief tagged "Ultra Hog". The saying "Go Ugly Early" has been associated with the aircraft in reference to calling in the A-10 early to support troops in ground combat.


title: Gini coefficient

text: In economics, the Gini coefficient ( ), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality or the wealth inequality within a nation or a social group. The Gini coefficient was developed by the statistician and sociologist Corrado Gini.


title: Gini coefficient

text: The Gini coefficient measures the inequality among values of a frequency distribution, such as the levels of income. A Gini coefficient of 0 reflects "perfect equality", where all income or wealth values are the same, while a Gini coefficient of 1 (or 100%) reflects "maximal inequality" among values. For example, if everyone has the same income, the Gini coefficient will be 0. In contrast, if for a large number of people only one person has all the income or consumption and all others have none, the Gini coefficient will be 1.


title: Gini coefficient

text: The Gini coefficient was proposed by Corrado Gini as a measure of inequality of income or wealth. For OECD countries, in the late 20th century, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 and 0.49, with Slovenia being the lowest and Mexico the highest. African countries had the highest pre-tax Gini coefficients in 2008–2009, with South Africa having the world's highest, variously estimated to be 0.63 to 0.7, although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation. The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.


title: Gini coefficient

text: There are some issues in interpreting a Gini coefficient; the same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population or with an increased birth rate experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.


title: Gini coefficient

text: The Gini coefficient was developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variability and Mutability" (). Building on the work of American economist Max Lorenz, Gini proposed that the difference between the hypothetical straight line depicting perfect equality, and the actual line depicting people's incomes, be used as a measure of inequality.


title: Gini coefficient

text: The Gini coefficient is an index for the degree of inequality in the distribution of income/wealth, used to estimate how far a country's wealth or income distribution deviates from an equal distribution.


title: Gini coefficient

text: The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y-axis) that is cumulatively earned by the bottom "x" of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked "A" in the diagram) over the total area under the line of equality (marked "A" and "B" in the diagram); i.e., . If there are no negative incomes, it is also equal to 2"A" and to due to the fact that .


title: Gini coefficient

text: Suppose all people have non-negative income (or wealth, as the case may be). In that case, the Gini coefficient can theoretically range from 0 (complete equality) to 1 (complete inequality) and is sometimes expressed as a percentage ranging between 0 and 100. If negative values are possible (such as the wealth of people with debts), then the Gini coefficient could theoretically be more than 1. Usually, the mean (or total) is assumed to be positive, which rules out a Gini coefficient of less than zero.


title: Gini coefficient

text: An alternative approach is to define the Gini coefficient as half of the relative mean absolute difference, which is mathematically equivalent to the definition based on the Lorenz curve. The mean absolute difference is the average absolute difference of all pairs of items of the population, and the relative mean absolute difference is the mean absolute difference divided by the average, formula_1, to normalize for scale. If "x" is the wealth or income of person "i", and there are "n" persons, then the Gini coefficient "G" is given by:


title: Gini coefficient

text: When the income (or wealth) distribution is given as a continuous probability density function "p"("x"), the Gini coefficient is again half of the relative mean absolute difference:


title: Gini coefficient

text: where formula_4 is the mean of the distribution, and the lower limits of integration may be replaced by zero when all incomes are positive.


title: Gini coefficient

text: While the income distribution of any particular country will not always follow theoretical models, in reality, these models give a qualitative understanding of the income distribution in a nation given the Gini coefficient.


title: Gini coefficient

text: The extreme cases are represented by the "most equal" society in which every person receives the same income () and the "most unequal" society (composed of "N" individuals) where a single person receives 100% of the total income and the remaining people receive none ().


title: Gini coefficient

text: A simplified case distinguishes just two levels of income, low and high. If the high income group is a proportion "u" of the population and earns a proportion "f" of all income, then the Gini coefficient is . A more graded distribution with these same values "u" and "f" will always have a higher Gini coefficient than .


title: Gini coefficient

text: An example case in which the richest 20% of the population have 80% of all income (see Pareto principle) would lead to an income Gini coefficient of at least 60%.


title: Gini coefficient

text: Another example case in which 1% of all the world's population owns 50% of all wealth, would result in a wealth Gini coefficient of at least 49%.


title: Gini coefficient

text: In some cases, this equation can be applied to calculate the Gini coefficient without direct reference to the Lorenz curve. For example, (taking "y" to indicate the income or wealth of a person or household):


title: Gini coefficient

text: Since the Gini coefficient is half the relative mean absolute difference, it can also be calculated using formulas for the relative mean absolute difference. For a random sample "S" consisting of values "y", "i" = 1 to "n", that are indexed in non-decreasing order ("y" ≤ "y"), the statistic:


title: Gini coefficient

text: is a consistent estimator of the population Gini coefficient, but is not, in general, unbiased. Like "G", has a simpler form:


title: Gini coefficient

text: There does not exist a sample statistic that is, in general, an unbiased estimator of the population Gini coefficient, like the relative mean absolute difference.


title: Gini coefficient

text: For a discrete probability distribution with probability mass function formula_9 formula_10, where formula_11 is the fraction of the population with income or wealth formula_12, the Gini coefficient is:


title: Gini coefficient

text: When the population is large, the income distribution may be represented by a continuous probability density function "f"("x") where "f"("x") "dx" is the fraction of the population with wealth or income in the interval "dx" about "x". If "F"("x") is the cumulative distribution function for "f"("x"):


title: Gini coefficient

text: then the Lorenz curve "L"("F") may then be represented as a function parametric in "L"("x") and "F"("x") and the value of "B" can be found by integration:


title: Gini coefficient

text: The Gini coefficient can also be calculated directly from the cumulative distribution function of the distribution "F"("y"). Defining μ as the mean of the distribution, and specifying that "F"("y") is zero for all negative values, the Gini coefficient is given by:


title: Gini coefficient

text: The latter result comes from integration by parts. (Note that this formula can be applied when there are negative values if the integration is taken from minus infinity to plus infinity.)


title: Gini coefficient

text: The Gini coefficient may be expressed in terms of the quantile function "Q"("F") (inverse of the cumulative distribution function: "Q"("F"("x")) = "x")


title: Gini coefficient

text: Since the Gini coefficient is independent of scale, if the distribution function can be expressed in the form "f(x,φ,a,b,c...)" where "φ" is a scale factor and "a,b,c..." are dimensionless parameters, then the Gini coefficient will be a function only of "a,b,c...". For example, for the exponential distribution, which is a function of only "x" and a scale parameter, the Gini coefficient is a constant, equal to 1/2.


title: Gini coefficient

text: For some functional forms, the Gini index can be calculated explicitly. For example, if "y" follows a log-normal distribution with the standard deviation of logs equal to formula_25, then formula_26 where formula_27 is the error function ( since formula_28, where formula_29 is the cumulative distribution function of a standard normal distribution). In the table below, some examples for probability density functions with support on formula_30 are shown. The Dirac delta distribution represents the case where everyone has the same wealth (or income); it implies no variations between incomes.


title: Gini coefficient

text: Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given. In that case, the Gini coefficient can be approximated using various techniques for interpolating the missing values of the Lorenz curve. If ("X", "Y") are the known points on the Lorenz curve, with the "X" indexed in increasing order ("X" < "X"), so that:


title: Gini coefficient

text: If the Lorenz curve is approximated on each interval as a line between consecutive points, then the area B can be approximated with trapezoids and:


title: Gini coefficient

text: is the resulting approximation for G. More accurate results can be obtained using other methods to approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals or building an appropriately smooth approximation to the underlying distribution function that matches the known data. If the population mean and boundary values for each interval are also known, these can also often be used to improve the accuracy of the approximation.


title: Gini coefficient

text: The Gini coefficient calculated from a sample is a statistic, and its standard error, or confidence intervals for the population Gini coefficient, should be reported. These can be calculated using bootstrap techniques, mathematically complicated and computationally demanding even in an era of fast computers. Economist Tomson Ogwang made the process more efficient by setting up a "trick regression model" in which respective income variables in the sample are ranked, with the lowest income being allocated rank 1. The model then expresses the rank (dependent variable) as the sum of a constant "A" and a normal error term whose variance is inversely proportional to "y":


title: Gini coefficient

text: Thus, "G" can be expressed as a function of the weighted least squares estimate of the constant "A" and that this can be used to speed up the calculation of the jackknife estimate for the standard error. Economist David Giles argued that the standard error of the estimate of "A" can be used to derive the estimate of "G" directly without using a jackknife. This method only requires using ordinary least squares regression after ordering the sample data. The results compare favorably with the estimates from the jackknife with agreement improving with increasing sample size.


title: Gini coefficient

text: However, it has been argued that this depends on the model's assumptions about the error distributions and the independence of error terms. These assumptions are often not valid for real data sets. There is still ongoing debate surrounding this topic.


title: Gini coefficient

text: Guillermina Jasso and Angus Deaton independently proposed the following formula for the Gini coefficient:


title: Gini coefficient

text: where formula_37 is mean income of the population, P is the income rank P of person i, with income X, such that the richest person receives a rank of 1 and the poorest a rank of "N". This effectively gives higher weight to poorer people in the income distribution, which allows the Gini to meet the Transfer Principle. Note that the Jasso-Deaton formula rescales the coefficient so that its value is one if all the formula_38 are zero except one. Note however Allison's reply on the need to divide by N² instead.


title: Gini coefficient

text: The Gini coefficient and other standard inequality indices reduce to a common form. Perfect equality—the absence of inequality—exists when and only when the inequality ratio, formula_39, equals 1 for all j units in some population (for example, there is perfect income equality when everyone's income formula_40 equals the mean income formula_41, so that formula_42 for everyone). Measures of inequality, then, are measures of the average deviations of the formula_42 from 1; the greater the average deviation, the greater the inequality. Based on these observations the inequality indices have this common form:


title: Gini coefficient

text: where "p" weights the units by their population share, and "f"("r") is a function of the deviation of each unit's "r" from 1, the point of equality. The insight of this generalised inequality index is that inequality indices differ because they employ different functions of the distance of the inequality ratios (the "r") from 1.


title: Gini coefficient

text: Gini coefficients of income are calculated on a market income and a disposable income basis. The Gini coefficient on market income—sometimes referred to as a pre-tax Gini coefficient—is calculated on income before taxes and transfers. It measures inequality in income without considering the effect of taxes and social spending already in place in a country. The Gini coefficient on disposable income—sometimes referred to as the after-tax Gini coefficient—is calculated on income after taxes and transfers. It measures inequality in income after considering the effect of taxes and social spending already in place in a country.


title: Gini coefficient

text: For OECD countries over the 2008–2009 period, the Gini coefficient (pre-taxes and transfers) for a total population ranged between 0.34 and 0.53, with South Korea the lowest and Italy the highest. The Gini coefficient (after-taxes and transfers) for a total population ranged between 0.25 and 0.48, with Denmark the lowest and Mexico the highest. For the United States, the country with the largest population among OECD countries, the pre-tax Gini index was 0.49, and the after-tax Gini index was 0.38 in 2008–2009. The OECD average for total populations in OECD countries was 0.46 for the pre-tax income Gini index and 0.31 for the after-tax income Gini index. Taxes and social spending that were in place in 2008–2009 period in OECD countries significantly lowered effective income inequality, and in general, "European countries—especially Nordic and Continental welfare states—achieve lower levels of income inequality than other countries."


title: Gini coefficient

text: Using the Gini can help quantify differences in welfare and compensation policies and philosophies. However, it should be borne in mind that the Gini coefficient can be misleading when used to make political comparisons between large and small countries or those with different immigration policies (see limitations section).


title: Gini coefficient

text: The Gini coefficient for the entire world has been estimated by various parties to be between 0.61 and 0.68. The graph shows the values expressed as a percentage in their historical development for a number of countries.


title: Gini coefficient

text: According to UNICEF, Latin America and the Caribbean region had the highest net income Gini index in the world at 48.3, on an unweighted average basis in 2008. The remaining regional averages were: sub-Saharan Africa (44.2), Asia (40.4), Middle East and North Africa (39.2), Eastern Europe and Central Asia (35.4), and High-income Countries (30.9). Using the same method, the United States is claimed to have a Gini index of 36, while South Africa had the highest income Gini index score of 67.8.


title: Gini coefficient

text: Taking income distribution of all human beings, worldwide income inequality has been constantly increasing since the early 19th century. There was a steady increase in the global income inequality Gini score from 1820 to 2002, with a significant increase between 1980 and 2002. This trend appears to have peaked and begun a reversal with rapid economic growth in emerging economies, particularly in the large populations of BRIC countries.


title: Gini coefficient

text: The table below presents the estimated world income Gini coefficients over the last 200 years, as calculated by Milanovic.


title: Gini coefficient

text: More detailed data from similar sources plots a continuous decline since 1988. This is attributed to globalization increasing incomes for billions of poor people, mostly in countries like China and India. Developing countries like Brazil have also improved basic services like health care, education, and sanitation; others like Chile and Mexico have enacted more progressive tax policies.


title: Gini coefficient

text: The Gini coefficient is widely used in fields as diverse as sociology, economics, health science, ecology, engineering, and agriculture. For example, in social sciences and economics, in addition to income Gini coefficients, scholars have published education Gini coefficients and opportunity Gini coefficients.


title: Gini coefficient

text: Education Gini index estimates the inequality in education for a given population. It is used to discern trends in social development through educational attainment over time. A study across 85 countries by three World Bank economists, Vinod Thomas, Yan Wang, and Xibo Fan, estimated Mali had the highest education Gini index of 0.92 in 1990 (implying very high inequality in educational attainment across the population), while the United States had the lowest education inequality Gini index of 0.14. Between 1960 and 1990, China, India and South Korea had the fastest drop in education inequality Gini Index. They also claim education Gini index for the United States slightly increased over the 1980–1990 period.


title: Gini coefficient

text: Similar in concept to the Gini income coefficient, the Gini opportunity coefficient measures inequality in opportunities. The concept builds on Amartya Sen's suggestion that inequality coefficients of social development should be premised on the process of enlarging people's choices and enhancing their capabilities, rather than on the process of reducing income inequality. Kovacevic, in a review of the Gini opportunity coefficient, explained that the coefficient estimates how well a society enables its citizens to achieve success in life where the success is based on a person's choices, efforts and talents, not his background defined by a set of predetermined circumstances at birth, such as gender, race, place of birth, parent's income and circumstances beyond the control of that individual.


title: Gini coefficient

text: In 2003, Roemer reported Italy and Spain exhibited the largest opportunity inequality Gini index amongst advanced economies.


title: Gini coefficient

text: In 1978, Anthony Shorrocks introduced a measure based on income Gini coefficients to estimate income mobility. This measure, generalized by Maasoumi and Zandvakili, is now generally referred to as Shorrocks index, sometimes as Shorrocks mobility index or Shorrocks rigidity index. It attempts to estimate whether the income inequality Gini coefficient is permanent or temporary and to what extent a country or region enables economic mobility to its people so that they can move from one (e.g., bottom 20%) income quantile to another (e.g., middle 20%) over time. In other words, the Shorrocks index compares inequality of short-term earnings, such as the annual income of households, to inequality of long-term earnings, such as 5-year or 10-year total income for the same households.


title: Gini coefficient

text: Shorrocks index is calculated in several different ways, a common approach being from the ratio of income Gini coefficients between short-term and long-term for the same region or country.


title: Gini coefficient

text: A 2010 study using social security income data for the United States since 1937 and Gini-based Shorrock's indices concludes that income mobility in the United States has had a complicated history, primarily due to the mass influx of women into the American labor force after World War II. Income inequality and income mobility trends have been different for men and women workers between 1937 and the 2000s. When men and women are considered together, the Gini coefficient-based Shorrocks index trends imply long-term income inequality has been substantially reduced among all workers, in recent decades for the United States. Other scholars, using just 1990s data or other short periods have come to different conclusions. For example, Sastre and Ayala conclude from their study of income Gini coefficient data between 1993 and 1998 for six developed economies that France had the least income mobility, Italy the highest, and the United States and Germany intermediate levels of income mobility over those five years.


title: Gini coefficient

text: The Gini coefficient has features that make it useful as a measure of dispersion in a population, and inequalities in particular.


title: Gini coefficient

text: The Gini coefficient is a relative measure. The Gini coefficient of a developing country can rise (due to increasing inequality of income) even when the number of people in absolute poverty decreases. This is because the Gini coefficient measures relative, not absolute, wealth. Changing income inequality, measured by Gini coefficients, can be due to structural changes in a society such as growing population (increased birth rates, aging populations, increased divorce rates, extended family households splitting into nuclear families, emigration, immigration) and income mobility. Gini coefficients are simple, and this simplicity can lead to oversights and can confuse the comparison of different populations; for example, while both Bangladesh (per capita income of $1,693) and the Netherlands (per capita income of $42,183) had an income Gini coefficient of 0.31 in 2010, the quality of life, economic opportunity and absolute income in these countries are very different, i.e. countries may have identical Gini coefficients, but differ greatly in wealth. Basic necessities may be available to all in a developed economy, while in an undeveloped economy with the same Gini coefficient, basic necessities may be unavailable to most or unequally available due to lower absolute wealth.


title: Gini coefficient

text: Even when the total income of a population is the same, in certain situations two countries with different income distributions can have the same Gini index (e.g. cases when income Lorenz Curves cross). Table A illustrates one such situation. Both countries have a Gini coefficient of 0.2, but the average income distributions for household groups are different. As another example, in a population where the lowest 50% of individuals have no income, and the other 50% have equal income, the Gini coefficient is 0.5; whereas for another population where the lowest 75% of people have 25% of income and the top 25% have 75% of the income, the Gini index is also 0.5. Economies with similar incomes and Gini coefficients can have very different income distributions. Bellù and Liberati claim that ranking income inequality between two populations is not always possible based on their Gini indices. Similarly, computational social scientist Fabian Stephany illustrates that income inequality within the population, e.g., in specific socio-economic groups of same age and education, also remains undetected by conventional Gini indices.


title: Gini coefficient

text: A Gini index does not contain information about absolute national or personal incomes. Populations can simultaneously have very low-income Gini indices and very high wealth Gini indexes. By measuring inequality in income, the Gini ignores the differential efficiency of the use of household income. By ignoring wealth (except as it contributes to income), the Gini can create the appearance of inequality when the people compared are at different stages in their life. Wealthy countries such as Sweden can show a low Gini coefficient for the disposable income of 0.31, thereby appearing equal, yet have a very high Gini coefficient for wealth of 0.79 to 0.86, suggesting an extremely unequal wealth distribution in its society. These factors are not assessed in income-based Gini.


title: Gini coefficient

text: Gini index has a downward-bias for small populations. Counties or states or countries with small populations and less diverse economies will tend to report small Gini coefficients. For economically diverse large population groups, a much higher coefficient is expected than for each of its regions. For example, taking the world economy as a whole and income distribution for all human beings, different scholars estimate the global Gini index to range between 0.61 and 0.68.


title: Gini coefficient

text: As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low granularity) will usually yield a lower Gini coefficient than twenty 5% quantiles (high granularity) for the same distribution. Philippe Monfort has shown that using inconsistent or unspecified granularity limits the usefulness of Gini coefficient measurements.


title: Gini coefficient

text: The Gini coefficient measure gives different results when applied to individuals instead of households, for the same economy and same income distributions. If household data is used, the measured value of income Gini depends on how the household is defined. The comparison is not meaningful when different populations are not measured with consistent definitions.


title: Gini coefficient

text: Deininger and Squire (1996) show that the income Gini coefficient based on individual income rather than household income is different. For example, for the United States, they found that the individual income-based Gini index was 0.35, while for France, 0.43. According to their individual-focused method, in the 108 countries they studied, South Africa had the world's highest Gini coefficient at 0.62, Malaysia had Asia's highest Gini coefficient at 0.5, Brazil the highest at 0.57 in Latin America and the Caribbean region, and Turkey the highest at 0.5 in OECD countries.


title: Gini coefficient

text: Expanding on the importance of life-span measures, the Gini coefficient as a point-estimate of equality at a certain time ignores life-span changes in income. Typically, increases in the proportion of young or old members of a society will drive apparent changes in equality simply because people generally have lower incomes and wealth when they are young than when they are old. Because of this, factors such as age distribution within a population and mobility within income classes can create the appearance of inequality when none exist, taking into account demographic effects. Thus a given economy may have a higher Gini coefficient at any timepoint compared to another, while the Gini coefficient calculated over individuals' lifetime income is lower than the apparently more equal (at a given point in time) economy's. Essentially, what matters is not just inequality in any particular year but the distribution composition over time.


title: Gini coefficient

text: Billionaire Thomas Kwok claimed the income Gini coefficient for Hong Kong has been high (0.434 in 2010), in part because of structural changes in its population. Over recent decades, Hong Kong has witnessed increasing numbers of small households, elderly households and elderly living alone. The combined income is now split into more households. Many older people live separate from their children in Hong Kong. These social changes have caused substantial changes in household income distribution. The income Gini coefficient, claims Kwok, does not discern these structural changes in its society. Household money income distribution for the United States, summarized in Table C of this section, confirms that this issue is not limited to just Hong Kong. According to the US Census Bureau, between 1979 and 2010, the population of the United States experienced structural changes in overall households; the income for all income brackets increased in inflation-adjusted terms, household income distributions shifted into higher income brackets over time, while the income Gini coefficient increased.


title: Gini coefficient

text: Another limitation of the Gini coefficient is that it is not a proper measure of egalitarianism, as it only measures income dispersion. For example, suppose two equally egalitarian countries pursue different immigration policies. In that case, the country accepting a higher proportion of low-income or impoverished migrants will report a higher Gini coefficient and, therefore, may exhibit more income inequality.


title: Gini coefficient

text: Some countries distribute benefits that are difficult to value. Countries that provide subsidized housing, medical care, education or other such services are difficult to value objectively, as it depends on the quality and extent of the benefit. In absence of a free market, valuing these income transfers as household income is subjective. The theoretical model of the Gini coefficient is limited to accepting correct or incorrect subjective assumptions.


title: Gini coefficient

text: In subsistence-driven and informal economies, people may have significant income in other forms than money, for example, through subsistence farming or bartering. These income tend to accrue to the segment of population below the poverty line or very poor in emerging and transitional economy countries such as those in sub-Saharan Africa, Latin America, Asia and Eastern Europe. Informal economy accounts for over half of global employment and as much as 90 per cent of employment in some of the poorer sub-Saharan countries with high official Gini inequality coefficients. Schneider et al., in their 2010 study of 162 countries, report about 31.2%, or about $20 trillion, of world's GDP is informal. In developing countries, the informal economy predominates for all income brackets except the richer, urban upper-income bracket populations. Even in developed economies, 8% (United States) to 27% (Italy) of each nation's GDP is informal. The resulting informal income predominates as a livelihood activity for those in the lowest income brackets. The value and distribution of the incomes from informal or underground economy is difficult to quantify, making true income Gini coefficients estimates difficult. Different assumptions and quantifications of these incomes will yield different Gini coefficients.


title: Gini coefficient

text: Gini has some mathematical limitations as well. It is not additive and different sets of people cannot be averaged to obtain the Gini coefficient of all the people in the sets.


title: Gini coefficient

text: Given the limitations of the Gini coefficient, other statistical methods are used in combination or as an alternative measure of population dispersity. For example, "entropy measures" are frequently used (e.g. the Atkinson index or the Theil Index and Mean log deviation as special cases of the generalized entropy index). These measures attempt to compare the distribution of resources by intelligent agents in the market with a maximum entropy random distribution, which would occur if these agents acted like non-interacting particles in a closed system following the laws of statistical physics.


title: Gini coefficient

text: There is a summary measure of the diagnostic ability of a binary classifier system that is also called the "Gini coefficient", which is defined as twice the area between the receiver operating characteristic (ROC) curve and its diagonal. It is related to the AUC (Area Under the ROC Curve) measure of performance given by formula_45 and to Mann–Whitney U. Although both Gini coefficients are defined as areas between certain curves and share certain properties, there is no simple direct relationship between the Gini coefficient of statistical dispersion and the Gini coefficient of a classifier.


title: Gini coefficient

text: The Gini index is also related to the Pietra index — both of which measure statistical heterogeneity and are derived from the Lorenz curve and the diagonal line.


title: Gini coefficient

text: In certain fields such as ecology, inverse Simpson's index formula_46 is used to quantify diversity, and this should not be confused with the Simpson index formula_47. These indicators are related to Gini. The inverse Simpson index increases with diversity, unlike the Simpson index and Gini coefficient, which decrease with diversity. The Simpson index is in the range [0, 1], where 0 means maximum and 1 means minimum diversity (or heterogeneity). Since diversity indices typically increase with increasing heterogeneity, the Simpson index is often transformed into inverse Simpson, or using the complement formula_48, known as the Gini-Simpson Index.


title: Gini coefficient

text: In recent decades, researchers have attempted to estimate Gini coefficients for pre-20th century societies. In the absence of household income surveys and income taxes, scholars have relied on proxy variables. These include wealth taxes in medieval European city states, patterns of landownership in Roman Egypt, variation of the size of houses in societies from ancient Greece to Aztec Mexico, and inheritance and dowries in Babylonian society. Other data does not directly document variations in wealth or income but are known to reflect inequality, such as the ratio of rents to wages or of labor to capital.


title: Gini coefficient

text: Although the Gini coefficient is most popular in economics, it can, in theory, be applied in any field of science that studies a distribution. For example, in ecology, the Gini coefficient has been used as a measure of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals. In health, it has been used as a measure of the inequality of health-related quality of life in a population. In education, it has been used as a measure of the inequality of universities. In chemistry it has been used to express the selectivity of protein kinase inhibitors against a panel of kinases. In engineering, it has been used to evaluate the fairness achieved by Internet routers in scheduling packet transmissions from different flows of traffic.


title: Gini coefficient

text: The Gini coefficient is sometimes used for the measurement of the discriminatory power of rating systems in credit risk management.


title: Gini coefficient

text: A 2005 study accessed US census data to measure home computer ownership and used the Gini coefficient to measure inequalities amongst whites and African Americans. Results indicated that although decreasing overall, home computer ownership inequality was substantially smaller among white households.


title: Gini coefficient

text: A 2016 peer-reviewed study titled Employing the Gini coefficient to measure participation inequality in treatment-focused Digital Health Social Networks illustrated that the Gini coefficient was helpful and accurate in measuring shifts in inequality, however as a standalone metric it failed to incorporate overall network size.


title: Gini coefficient

text: Discriminatory power refers to a credit risk model's ability to differentiate between defaulting and non-defaulting clients. The formula formula_49, in the calculation section above, may be used for the final model and at the individual model factor level to quantify the discriminatory power of individual factors. It is related to the accuracy ratio in population assessment models.


title: Gini coefficient

text: Kaminskiy and Krivtsov extended the concept of the Gini coefficient from economics to reliability theory and proposed a Gini–type coefficient that helps to assess the degree of aging of non−repairable systems or aging and rejuvenation of repairable systems. The coefficient is defined between -1 and 1 and can be used in both empirical and parametric life distributions. It takes negative values for the class of decreasing failure rate distributions and point processes with decreasing failure intensity rate and is positive for the increasing failure rate distributions and point processes with increasing failure intensity rate. The value of zero corresponds to the exponential life distribution or the Homogeneous Poisson Process.


title: Astrological sign

text: In Western astrology, astrological signs are the twelve 30-degree sectors that make up Earth's 360-degree orbit around the Sun. The signs enumerate from the first day of spring, known as the First Point of Aries, which is the vernal equinox. The astrological signs are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. The Western zodiac originated in Babylonian astrology, and was later influenced by the Hellenistic culture. Each sign was named after a constellation the sun annually moved through while crossing the sky. This observation is emphasized in the simplified and popular sun sign astrology. Over the centuries, Western astrology's zodiacal divisions have shifted out of alignment with the constellations they were named after by axial precession of the Earth while Hindu astrology measurements correct for this shifting. Astrology (i.e. a system of omina based on celestial appearances) was developed in Chinese and Tibetan cultures as well but these astrologies are not based upon the zodiac but deal with the whole sky.


title: Astrological sign

text: Astrology is a pseudoscience. Scientific investigations of the theoretical basis and experimental verification of claims have shown it to have no scientific validity or explanatory power. More plausible explanations for the apparent correlation between personality traits and birth months exist, such as the influence of seasonal birth in humans.


title: Astrological sign

text: According to astrology, celestial phenomena relate to human activity on the principle of "as above, so below", so that the signs are held to represent characteristic modes of expression. Scientific astronomy used the same sectors of the ecliptic as Western astrology until the 19th century.


title: Astrological sign

text: Various approaches to measuring and dividing the sky are currently used by differing systems of astrology, although the tradition of the Zodiac's names and symbols remain mostly consistent. Western astrology measures from Equinox and Solstice points (points relating to equal, longest, and shortest days of the tropical year), while Hindu astrology measures along the equatorial plane (sidereal year).


title: Astrological sign

text: Western astrology is a direct continuation of Hellenistic astrology as recorded in Ptolemy's Tetrabiblos in the 2nd century. Hellenistic astrology in turn was partly based on concepts from Babylonian tradition. Specifically, the division of the ecliptic in twelve equal sectors is a Babylonian conceptual construction. This division of the ecliptic originated in the Babylonian "ideal calendar" found in the old compendium MUL.APIN and its combination with the Babylonian lunar calendar, represented as the "path of the moon" in MUL.APIN. In a way, the zodiac is the idealisation of an ideal lunar calendar.


title: Astrological sign

text: By the 4th century BC, Babylonian astronomy and its system of celestial omens influenced the culture of ancient Greece, as did the astronomy of Egypt by late 2nd century BC. This resulted, unlike the Mesopotamian tradition, in a strong focus on the birth chart of the individual and the creation of Horoscopic astrology, employing the use of the Ascendant (the rising degree of the ecliptic, at the time of birth), and of the twelve houses. Association of the astrological signs with Empedocles' four classical elements was another important development in the characterization of the twelve signs.


title: Astrological sign

text: The body of the Hellenistic astrological tradition as it stood by the 2nd century is described in Ptolemy's "Tetrabiblos". This is the seminal work for later astronomical tradition not only in the West but also in India and the Islamic sphere and has remained a reference for almost seventeen centuries as later traditions made few substantial changes to its core teachings.


title: Astrological sign

text: The following table shows the approximate dates of the twelve astrological signs, along with the classical and modern rulerships of each sign. By definition, Aries starts at the First Point of Aries which is the location of the Sun at the March equinox. The precise date of the Equinox varies from year to year but is always between 19 March and 21 March. The consequence is the start date of Aries and therefore the start date of all the other signs can change slightly from year to year. The following Western astrology table enumerates the twelve divisions of celestial longitude with the Latin names. The longitude intervals, are treated as closed for the first endpoint ("a") and open for the second ("b") – for instance, 30° of longitude is the first point of Taurus, not part of Aries. The signs are occasionally numbered 0 through 11 in place of symbols in astronomical works.


title: Astrological sign

text: The twelve signs each have opposites, resulting in six opposite couples. Fire and air elements are opposites, and earth and water elements are opposites. Spring signs are opposite to autumn ones, winter signs are opposite to summer ones and vice versa.


title: Astrological sign

text: In Western astrology, the polarity divides the zodiac in half and refers to the alignment of a sign's energy as either positive or negative, with various attributes associated to them as a result. Positive polarity signs, also called active, yang, expressive, or masculine signs, are the six odd-numbered signs of the zodiac: Aries, Gemini, Leo, Libra, Sagittarius, and Aquarius. Positive signs make up the fire and air triplicities. Negative polarity signs, also called passive, yin, receptive, or feminine signs, are the six even-numbered signs of the zodiac: Taurus, Cancer, Virgo, Scorpio, Capricorn, and Pisces. Negative signs make up the earth and water triplicities.


title: Astrological sign

text: The modality or mode of a given sign refers to its position in the season it is found in. Each of the four elements manifests in three modalities: cardinal, fixed, and mutable. Since each modality comprehends four signs, they are also known as Quadruplicities. For example, the sign Aries is found in the first month of spring in the Northern Hemisphere, so practitioners of astrology describe it as having a cardinal modality. The combination of element and modality provides the signs with their unique characterizations. For instance, Capricorn is the cardinal earth sign, impressing its association with action (cardinal modality) in the material world (earth element).


title: Astrological sign

text: The Greek philosopher Empedocles identified fire, earth, air, and water as elements in the fifth-century BC. He explained the nature of the universe as an interaction of two opposing principles, love and strife, manipulate the elements into different mixtures that produce the different natures of things. He stated all the elements are equal, the same age, rule their own provinces, and possess their own individual character. Empedocles said that those born with nearly equal proportions of the elements are more intelligent and have the most exact perceptions.