title: Krishna

text: The use of the term bhakti, meaning devotion, is not confined to any one deity. However, Krishna is an important and popular focus of the devotionalism tradition within Hinduism, particularly among the Vaishnava Krishnaite sects. Devotees of Krishna subscribe to the concept of "lila", meaning 'divine play', as the central principle of the universe. It is a form of bhakti yoga, one of three types of yoga discussed by Krishna in the "Bhagavad Gita".


title: Krishna

text: The bhakti movements devoted to Krishna became prominent in southern India in the 7th to 9thcenturies CE. The earliest works included those of the Alvar saints of Tamil Nadu. A major collection of their works is the "Divya Prabandham". Alvar Andal's popular collection of songs Tiruppavai, in which she conceives of herself as a gopi, is the most famous of the oldest works in this genre.


title: Krishna

text: The movement originated in South India during the 7th century CE, spreading northwards from Tamil Nadu through Karnataka and Maharashtra; by the 15thcentury, it was established in Bengal and northern India. Early Krishnaite Bhakti pioneers included Nimbarkacharya (12th or 13thcentury CE), but most emerged later, including Vallabhacharya (15thcentury CE) and Chaitanya Mahaprabhu. They started their own schools, namely Nimbarka Sampradaya, Vallabha Sampradaya, and Gaudiya Vaishnavism, with Krishna and Radha as the supreme gods. In addition, since the 15th century, flourished Tantric variety of Krishnaism, Vaishnava-Sahajiya, is linked to the Bengali poet Chandidas.


title: Krishna

text: In the Deccan, particularly in Maharashtra, saint poets of the Warkari sect such as Dnyaneshwar, Namdev, Janabai, Eknath, and Tukaram promoted the worship of Vithoba, a local form of Krishna, from between the 13th to 18th century. Before the Warkari tradition, Krishna devotion became well established in Maharashtra due to the rise of the Mahanubhava Sampradaya founded by Sarvajna Chakradhara. The Pranami Sampradaya emerged in the 17th century in Gujarat, based on the Krishna-focussed syncretist Hindu-Islamic teachings of Devchandra Maharaj and his famous successor, Mahamati Prannath. In southern India, Purandara Dasa and Kanakadasa of Karnataka composed songs devoted to the Krishna image of Udupi. Rupa Goswami of Gaudiya Vaishnavism has compiled a comprehensive summary of bhakti called Bhakti-rasamrita-sindhu.


title: Krishna

text: In South India, the acharyas of the Sri Sampradaya have written reverently about Krishna in most of their works, including the Thiruppavai by Andal and Gopala Vimshati by Vedanta Desika.


title: Krishna

text: Tamil Nadu, Karnataka, Andhra Pradesh, and Kerala states have many major Krishna temples, and Janmashtami is one of the widely celebrated festivals in South India.


title: Krishna

text: By 1965, the "Krishna-bhakti" movement had spread outside India after Bhaktivedanta Swami Prabhupada (as instructed by his guru, Bhaktisiddhanta Sarasvati Thakura) travelled from his homeland in West Bengal to New York City. A year later, in 1966, after gaining many followers, he was able to form the International Society for Krishna Consciousness (ISKCON), popularly known as the Hare Krishna movement. The purpose of this movement was to write about Krishna in English and to share the Gaudiya Vaishnava philosophy with people in the Western world by spreading the teachings of the saint Chaitanya Mahaprabhu. In the biographies of Chaitanya Mahaprabhu, the mantra he received when he was given diksha or initiation in Gaya was the six-word verse of the "Kali-Santarana Upanishad", namely "Hare Krishna Hare Krishna, Krishna Krishna Hare Hare; Hare Rama Hare Rama, Rama Rama Hare Hare". In the Gaudiya tradition, it is the "maha-mantra", or great mantra, about Krishna bhakti. Its chanting was known as "hari-nama sankirtana".


title: Krishna

text: The "maha-mantra" gained the attention of George Harrison and John Lennon of The Beatles fame, and Harrison produced a 1969 recording of the mantra by devotees from the London Radha Krishna Temple. Titled "Hare Krishna Mantra", the song reached the top twenty on the UK music charts and was also successful in West Germany and Czechoslovakia. The mantra of the Upanishad thus helped bring Bhaktivedanta and ISKCON ideas about Krishna into the West. ISCKON has built many Krishna temples in the West, as well as other locations such as South Africa.


title: Krishna

text: Krishna is found in Southeast Asian history and art, but to a far lesser extent than Shiva, Durga, Nandi, Agastya, and Buddha. In temples ("candi") of the archaeological sites in hilly volcanic Java, Indonesia, temple reliefs do not portray his pastoral life or his role as the erotic lover, nor do the historic Javanese Hindu texts. Rather, either his childhood or the life as a king and Arjuna's companion have been more favored. The most elaborate temple arts of Krishna is found in a series of "Krsnayana" reliefs in the Prambanan Hindu temple complex near Yogyakarta. These are dated to the 9thcentury CE. Krishna remained a part of the Javanese cultural and theological fabric through the 14thcentury, as evidenced by the 14th-century Penataran reliefs along with those of the Hindu god Rama in east Java, before Islam replaced Buddhism and Hinduism on the island.


title: Krishna

text: The medieval era arts of Vietnam and Cambodia feature Krishna. The earliest surviving sculptures and reliefs are from the 6th and 7thcenturies, and these include Vaishnavism iconography. According to John Guy, the curator and director of Southeast Asian arts at the Metropolitan Museum of Art, the Krishna Govardhana art from 6th/7th-century Vietnam at Danang, and 7th-century Cambodia at Phnom Da cave in Angkor Borei, are some of the most sophisticated of this era.


title: Krishna

text: Krishna's iconography has also been found in Thailand, along with those of Surya and Vishnu. For example, a large number of sculptures and icons have been found in the SiThep and Klangnai sites in the Phetchabun region of northern Thailand. These are dated to about the 7th and 8thcenturies, from both the Funan and Zhenla period archaeological sites.


title: Krishna

text: Indian dance and music theatre traces its origins and techniques to the ancient "Sama Veda" and "Natyasastra" texts. The stories enacted and the numerous choreographic themes are inspired by the mythologies and legends in Hindu texts, including Krishna-related literature such as "Harivamsa" and "Bhagavata Purana".


title: Krishna

text: The Krishna stories have played a key role in the history of Indian theatre, music, and dance, particularly through the tradition of "Rasaleela". These are dramatic enactments of Krishna's childhood, adolescence, and adulthood. One common scene involves Krishna playing flute in Rasa Leela, only to be heard by certain gopis (cowherd maidens), which is theologically supposed to represent divine call only heard by certain enlightened beings. Some of the text's legends have inspired secondary theatre literature such as the eroticism in Gita Govinda.


title: Krishna

text: Krishna-related literature such as the "Bhagavata Purana" accords a metaphysical significance to the performances and treats them as a religious ritual, infusing daily life with spiritual meaning, thus representing a good, honest, happy life. Similarly, Krishna-inspired performances aim to cleanse the hearts of faithful actors and listeners. Singing, dancing, and performing any part of "Krishna Lila" is an act of remembering the dharma in the text, as a form of "para bhakti" (supreme devotion). To remember Krishna at any time and in any art, asserts the text, is to worship the good and the divine.


title: Krishna

text: Classical dance styles such as Kathak, Odissi, Manipuri, Kuchipudi and Bharatanatyam in particular are known for their Krishna-related performances. Krisnattam (Krishnattam) traces its origins to Krishna legends, and is linked to another major classical Indian dance form called Kathakali. Bryant summarizes the influence of Krishna stories in the "Bhagavata Purana" as, "[it] has inspired more derivative literature, poetry, drama, dance, theatre and art than any other text in the history of Sanskrit literature, with the possible exception of the "Ramayana".


title: Krishna

text: The Palliyodam, a type of large built and used by Aranmula Parthasarathy Temple in Kerala for the annual water processions of Uthrattathi Jalamela and Valla Sadhya has the legend that it was designed by Lord Krishna and were made to look like Sheshanaga, the serpent on which Lord Vishnu rests.


title: Krishna

text: The Jainism tradition lists 63 "Śalākāpuruṣa" or notable figures which, amongst others, includes the twenty-four "Tirthankaras" (spiritual teachers) and nine sets of triads. One of these triads is Krishna as the "Vasudeva", Balarama as the "Baladeva", and Jarasandha as the "Prati-Vasudeva". In each age of the Jain cyclic time is born a "Vasudeva" with an elder brother termed the "Baladeva". Between the triads, "Baladeva" upholds the principle of non-violence, a central idea of Jainism. The villain is the "Prati-vasudeva", who attempts to destroy the world. To save the world, "Vasudeva-Krishna" has to forsake the non-violence principle and kill the "Prati-Vasudeva". The stories of these triads can be found in the "Harivamsa Purana" (8thcentury CE) of Jinasena (not be confused with its namesake, the addendum to "Mahābhārata") and the "Trishashti-shalakapurusha-charita" of Hemachandra.


title: Krishna

text: The story of Krishna's life in the "Puranas" of Jainism follows the same general outline as those in the Hindu texts, but in details, they are very different: they include Jain "Tirthankaras" as characters in the story, and generally are polemically critical of Krishna, unlike the versions found in the "Mahabharata", the "Bhagavata Purana", and the "Vishnu Purana". For example, Krishna loses battles in the Jain versions, and his "gopis" and his clan of Yadavas die in a fire created by an ascetic named Dvaipayana. Similarly, after dying from the hunter Jara's arrow, the Jaina texts state Krishna goes to the third hell in Jain cosmology, while his brother is said to go to the sixth heaven.


title: Krishna

text: Vimalasuri is attributed to be the author of the Jain version of the "Harivamsa Purana", but no manuscripts have been found that confirm this. It is likely that later Jain scholars, probably Jinasena of the 8thcentury, wrote a complete version of Krishna legends in the Jain tradition and credited it to the ancient Vimalasuri. Partial and older versions of the Krishna story are available in Jain literature, such as in the "Antagata Dasao" of the "Svetambara" "Agama" tradition.


title: Krishna

text: In other Jain texts, Krishna is stated to be a cousin of the twenty-second "Tirthankara", Neminatha. The Jain texts state that Neminatha taught Krishna all the wisdom that he later gave to Arjuna in the "Bhagavad Gita". According to Jeffery D. Long, a professor of religion known for his publications on Jainism, this connection between Krishna and Neminatha has been a historic reason for Jains to accept, read, and cite the "Bhagavad Gita" as a spiritually important text, celebrate Krishna-related festivals, and intermingle with Hindus as spiritual cousins.


title: Krishna

text: The story of Krishna occurs in the Jataka tales in Buddhism. The "Vidhurapandita Jataka" mentions "Madhura" (Sanskrit: Mathura), the "Ghata Jataka" mentions Kamsa, Devagabbha (Sk: Devaki), Upasagara or Vasudeva, Govaddhana (Sk: Govardhana), Baladeva (Balarama), and Kanha or Kesava (Sk: Krishna, Keshava).


title: Krishna

text: Like the Jaina versions of the Krishna legends, the Buddhist versions such as one in "Ghata Jataka" follow the general outline of the story, but are different from the Hindu versions as well. For example, the Buddhist legend describes Devagabbha (Devaki) to have been isolated in a palace built upon a pole after she is born, so no future husband could reach her. Krishna's father similarly is described as a powerful king, but who meets up with Devagabbha anyway, and to whom Kamsa gives away his sister Devagabbha in marriage. The siblings of Krishna are not killed by Kamsa, though he tries. In the Buddhist version of the legend, all of Krishna's siblings grow to maturity.


title: Krishna

text: Krishna and his siblings' capital becomes Dvaravati. The Arjuna and Krishna interaction is missing in the Jataka version. A new legend is included, wherein Krishna laments in uncontrollable sorrow when his son dies, and a Ghatapandita feigns madness to teach Krishna a lesson. The Jataka tale also includes internecine destruction among his siblings after they all get drunk. Krishna also dies in the Buddhist legend by the hand of a hunter named Jara, but while he is traveling to a frontier city. Mistaking Krishna for a pig, Jara throws a spear that fatally pierces his feet, causing Krishna great pain and then his death.


title: Krishna

text: At the end of this "Ghata-Jataka" discourse, the Buddhist text declares that Sariputta, one of the revered disciples of the Buddha in the Buddhist tradition, was incarnated as Krishna in his previous life to learn lessons on grief from the Buddha in his prior rebirth:


title: Krishna

text: While the Buddhist Jataka texts co-opt Krishna-Vasudeva and make him a student of the Buddha in his previous life, the Hindu texts co-opt the Buddha and make him an avatar of Vishnu. In Chinese Buddhism, Taoism and Chinese folk religion, the figure of Krishna has been amalgamated and merged with that of Nalakuvara to influence the formation of the god Nezha, who has taken on iconographic characteristics of Krishna such as being presented as a divine god-child and slaying a nāga in his youth.


title: Krishna

text: Krishna is mentioned as "Krishna Avtar" in the "Chaubis Avtar", a composition in Dasam Granth traditionally and historically attributed to Sikh Guru Gobind Singh.


title: Krishna

text: Within the Sikh-derived 19th-century Radha Soami movement, the followers of its founder Shiv Dayal Singh used to consider him the Living Master and incarnation of God (Lord Krishna/Vishnu).


title: Krishna

text: Baháʼís believe that Krishna was a "Manifestation of God", or one in a line of prophets who have revealed the Word of God progressively for a gradually maturing humanity. In this way, Krishna shares an exalted station with Abraham, Moses, Zoroaster, Buddha, Muhammad, Jesus, the Báb, and the founder of the Baháʼí Faith, Bahá'u'lláh.


title: Krishna

text: Ahmadiyya, a 20th-century Islamic movement, consider Krishna as one of their ancient prophets. Ghulam Ahmad stated that he was himself a prophet in the likeness of prophets such as Krishna, Jesus, and Muhammad, who had come to earth as a latter-day reviver of religion and morality.


title: Krishna

text: Krishna worship or reverence has been adopted by several new religious movements since the 19thcentury, and he is sometimes a member of an eclectic pantheon in occult texts, along with Greek, Buddhist, biblical, and even historical figures. For instance, Édouard Schuré, an influential figure in perennial philosophy and occult movements, considered Krishna a "Great Initiate", while Theosophists regard Krishna as an incarnation of Maitreya (one of the Masters of the Ancient Wisdom), the most important spiritual teacher for humanity along with Buddha.


title: Krishna

text: Krishna was canonised by Aleister Crowley and is recognised as a saint of Ecclesia Gnostica Catholica in the Gnostic Mass of Ordo Templi Orientis.


title: Normal distribution

text: In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is


title: Normal distribution

text: The parameter formula_3 is the mean or expectation of the distribution (and also its median and mode), while the parameter formula_18 is its standard deviation. The variance of the distribution is formula_6. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.


title: Normal distribution

text: Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal.


title: Normal distribution

text: Moreover, Gaussian distributions have some unique properties that are valuable in analytic studies. For instance, any linear combination of a fixed collection of normal deviates is a normal deviate. Many results and methods, such as propagation of uncertainty and least squares parameter fitting, can be derived analytically in explicit form when the relevant variables are normally distributed.


title: Normal distribution

text: A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's "t", and logistic distributions). For other names, see Naming.


title: Normal distribution

text: The univariate probability distribution is generalized for vectors in the multivariate normal distribution and for matrices in the matrix normal distribution.


title: Normal distribution

text: The simplest case of a normal distribution is known as the "standard normal distribution" or "unit normal distribution". This is a special case when formula_20 and formula_21, and it is described by this probability density function (or density):


title: Normal distribution

text: The variable formula_23 has a mean of 0 and a variance and standard deviation of 1. The density formula_24 has its peak formula_25 at formula_26 and inflection points at formula_27 and formula_28.


title: Normal distribution

text: Although the density above is most commonly known as the "standard normal," a few authors have used that term to describe other versions of the normal distribution. Carl Friedrich Gauss, for example, once defined the standard normal as


title: Normal distribution

text: Every normal distribution is a version of the standard normal distribution, whose domain has been stretched by a factor formula_18 (the standard deviation) and then translated by formula_3 (the mean value):


title: Normal distribution

text: If formula_36 is a standard normal deviate, then formula_37 will have a normal distribution with expected value formula_3 and standard deviation formula_18. This is equivalent to saying that the "standard" normal distribution formula_36 can be scaled/stretched by a factor of formula_18 and shifted by formula_3 to yield a different normal distribution, called formula_43. Conversely, if formula_43 is a normal deviate with parameters formula_3 and formula_6, then this formula_43 distribution can be re-scaled and shifted via the formula formula_48 to convert it to the "standard" normal distribution. This variate is also called the standardized form of formula_43.


title: Normal distribution

text: The probability density of the standard Gaussian distribution (standard normal distribution, with zero mean and unit variance) is often denoted with the Greek letter formula_50 (phi). The alternative form of the Greek letter phi, formula_51, is also used quite often.


title: Normal distribution

text: The normal distribution is often referred to as formula_52 or formula_53. Thus when a random variable formula_43 is normally distributed with mean formula_3 and standard deviation formula_18, one may write


title: Normal distribution

text: Some authors advocate using the precision formula_58 as the parameter defining the width of the distribution, instead of the deviation formula_18 or the variance formula_6. The precision is normally defined as the reciprocal of the variance, formula_61. The formula for the distribution then becomes


title: Normal distribution

text: This choice is claimed to have advantages in numerical computations when formula_18 is very close to zero, and simplifies formulas in some contexts, such as in the Bayesian inference of variables with multivariate normal distribution.


title: Normal distribution

text: Alternatively, the reciprocal of the standard deviation formula_64 might be defined as the "precision", in which case the expression of the normal distribution becomes


title: Normal distribution

text: According to Stigler, this formulation is advantageous because of a much simpler and easier-to-remember formula, and simple approximate formulas for the quantiles of the distribution.


title: Normal distribution

text: Normal distributions form an exponential family with natural parameters formula_66 and formula_67, and natural statistics "x" and "x". The dual expectation parameters for normal distribution are and .


title: Normal distribution

text: The cumulative distribution function (CDF) of the standard normal distribution, usually denoted with the capital Greek letter formula_68 (phi), is the integral


title: Normal distribution

text: The related error function formula_70 gives the probability of a random variable, with normal distribution of mean 0 and variance 1/2 falling in the range formula_71. That is:


title: Normal distribution

text: These integrals cannot be expressed in terms of elementary functions, and are often said to be special functions. However, many numerical approximations are known; see below for more.


title: Normal distribution

text: For a generic normal distribution with density formula_74, mean formula_3 and deviation formula_18, the cumulative distribution function is


title: Normal distribution

text: The complement of the standard normal CDF, formula_78, is often called the Q-function, especially in engineering texts. It gives the probability that the value of a standard normal random variable formula_43 will exceed formula_80: formula_81. Other definitions of the formula_82-function, all of which are simple transformations of formula_68, are also used occasionally.


title: Normal distribution

text: The graph of the standard normal CDF formula_68 has 2-fold rotational symmetry around the point (0,1/2); that is, formula_85. Its antiderivative (indefinite integral) can be expressed as follows:


title: Normal distribution

text: An asymptotic expansion of the CDF for large "x" can also be derived using integration by parts. For more, see Error function#Asymptotic expansion.


title: Normal distribution

text: A quick approximation to the standard normal distribution's CDF can be found by using a Taylor series approximation:


title: Normal distribution

text: About 68% of values drawn from a normal distribution are within one standard deviation "σ" away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. This fact is known as the 68-95-99.7 (empirical) rule, or the "3-sigma rule".


title: Normal distribution

text: More precisely, the probability that a normal deviate lies in the range between formula_90 and formula_91 is given by


title: Normal distribution

text: The quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard normal distribution is called the probit function, and can be expressed in terms of the inverse error function:


title: Normal distribution

text: The quantile formula_100 of the standard normal distribution is commonly denoted as formula_101. These values are used in hypothesis testing, construction of confidence intervals and Q–Q plots. A normal random variable formula_43 will exceed formula_103 with probability formula_104, and will lie outside the interval formula_105 with probability formula_106. In particular, the quantile formula_107 is 1.96; therefore a normal random variable will lie outside the interval formula_108 in only 5% of cases.


title: Normal distribution

text: The following table gives the quantile formula_101 such that formula_43 will lie in the range formula_105 with a specified probability formula_112. These values are useful to determine tolerance interval for sample averages and other statistical estimators with normal (or asymptotically normal) distributions. Note that the following table shows formula_113, not formula_100 as defined above.


title: Normal distribution

text: The normal distribution is the only distribution whose cumulants beyond the first two (i.e., other than the mean and variance) are zero. It is also the continuous distribution with the maximum entropy for a specified mean and variance. Geary has shown, assuming that the mean and variance are finite, that the normal distribution is the only distribution where the mean and variance calculated from a set of independent draws are independent of each other.


title: Normal distribution

text: The normal distribution is a subclass of the elliptical distributions. The normal distribution is symmetric about its mean, and is non-zero over the entire real line. As such it may not be a suitable model for variables that are inherently positive or strongly skewed, such as the weight of a person or the price of a share. Such variables may be better described by other distributions, such as the log-normal distribution or the Pareto distribution.


title: Normal distribution

text: The value of the normal distribution is practically zero when the value formula_80 lies more than a few standard deviations away from the mean (e.g., a spread of three standard deviations covers all but 0.27% of the total distribution). Therefore, it may not be an appropriate model when one expects a significant fraction of outliers—values that lie many standard deviations away from the mean—and least squares and other statistical inference methods that are optimal for normally distributed variables often become highly unreliable when applied to such data. In those cases, a more heavy-tailed distribution should be assumed and the appropriate robust statistical inference methods applied.


title: Normal distribution

text: The Gaussian distribution belongs to the family of stable distributions which are the attractors of sums of independent, identically distributed distributions whether or not the mean or variance is finite. Except for the Gaussian which is a limiting case, all stable distributions have heavy tails and infinite variance. It is one of the few distributions that are stable and that have probability density functions that can be expressed analytically, the others being the Cauchy distribution and the Lévy distribution.


title: Normal distribution

text: The normal distribution with density formula_118 (mean formula_3 and standard deviation formula_120) has the following properties:


title: Normal distribution

text: Furthermore, the density formula_51 of the standard normal distribution (i.e. formula_20 and formula_132) also has the following properties:


title: Normal distribution

text: The plain and absolute moments of a variable formula_43 are the expected values of formula_142 and formula_143, respectively. If the expected value formula_3 of formula_43 is zero, these parameters are called "central moments;" otherwise, these parameters are called "non-central moments." Usually we are interested only in moments with integer order formula_146.


title: Normal distribution

text: If formula_43 has a normal distribution, the non-central moments exist and are finite for any formula_112 whose real part is greater than −1. For any non-negative integer formula_112, the plain central moments are:


title: Normal distribution

text: Here formula_151 denotes the double factorial, that is, the product of all numbers from formula_94 to 1 that have the same parity as formula_153


title: Normal distribution

text: The central absolute moments coincide with plain moments for all even orders, but are nonzero for odd orders. For any non-negative integer formula_154


title: Normal distribution

text: The last formula is valid also for any non-integer formula_156 When the mean formula_157 the plain and absolute moments can be expressed in terms of confluent hypergeometric functions formula_158 and formula_159


title: Normal distribution

text: These expressions remain valid even if formula_112 is not an integer. See also generalized Hermite polynomials.


title: Normal distribution

text: The expectation of formula_43 conditioned on the event that formula_43 lies in an interval formula_164 is given by


title: Normal distribution

text: where formula_74 and formula_166 respectively are the density and the cumulative distribution function of formula_43. For formula_168 this is known as the inverse Mills ratio. Note that above, density formula_74 of formula_43 is used instead of standard normal density as in inverse Mills ratio, so here we have formula_6 instead of formula_18.


title: Normal distribution

text: The Fourier transform of a normal density formula_74 with mean formula_3 and standard deviation formula_18 is


title: Normal distribution

text: where formula_177 is the imaginary unit. If the mean formula_20, the first factor is 1, and the Fourier transform is, apart from a constant factor, a normal density on the frequency domain, with mean 0 and standard deviation formula_35. In particular, the standard normal distribution formula_51 is an eigenfunction of the Fourier transform.


title: Normal distribution

text: In probability theory, the Fourier transform of the probability distribution of a real-valued random variable formula_43 is closely connected to the characteristic function formula_182 of that variable, which is defined as the expected value of formula_183, as a function of the real variable formula_184 (the frequency parameter of the Fourier transform). This definition can be analytically extended to a complex-value variable formula_184. The relation between both is:


title: Normal distribution

text: The moment generating function of a real random variable formula_43 is the expected value of formula_188, as a function of the real parameter formula_184. For a normal distribution with density formula_74, mean formula_3 and deviation formula_18, the moment generating function exists and is equal to


title: Normal distribution

text: Since this is a quadratic polynomial in formula_184, only the first two cumulants are nonzero, namely the mean formula_3 and the variance formula_6.


title: Normal distribution

text: Within Stein's method the Stein operator and class of a random variable formula_198 are formula_199 and formula_200 the class of all absolutely continuous functions formula_201.


title: Normal distribution

text: In the limit when formula_18 tends to zero, the probability density formula_118 eventually tends to zero at any formula_204, but grows without limit if formula_205, while its integral remains equal to 1. Therefore, the normal distribution cannot be defined as an ordinary function when formula_206.


title: Normal distribution

text: However, one can define the normal distribution with zero variance as a generalized function; specifically, as Dirac's "delta function" formula_207 translated by the mean formula_3, that is formula_209


title: Normal distribution

text: Of all probability distributions over the reals with a specified mean formula_3 and variance formula_6, the normal distribution formula_52 is the one with maximum entropy. If formula_43 is a continuous random variable with probability density formula_118, then the entropy of formula_43 is defined as


title: Normal distribution

text: where formula_219 is understood to be zero whenever formula_220. This functional can be maximized, subject to the constraints that the distribution is properly normalized and has a specified variance, by using variational calculus. A function with two Lagrange multipliers is defined:


title: Normal distribution

text: where formula_118 is, for now, regarded as some density function with mean formula_3 and standard deviation formula_18.


title: Normal distribution

text: At maximum entropy, a small variation formula_225 about formula_118 will produce a variation formula_227 about formula_228 which is equal to 0:


title: Normal distribution

text: Since this must hold for any small formula_225, the term in brackets must be zero, and solving for formula_118 yields:


title: Normal distribution

text: Using the constraint equations to solve for formula_233 and formula_234 yields the density of the normal distribution:


title: Normal distribution

text: The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution. More specifically, where formula_248 are independent and identically distributed random variables with the same arbitrary distribution, zero mean, and variance formula_6 and formula_36 is their


title: Normal distribution

text: Then, as formula_94 increases, the probability distribution of formula_36 will tend to the normal distribution with zero mean and variance formula_6.


title: Normal distribution

text: The theorem can be extended to variables formula_256 that are not independent and/or not identically distributed if certain constraints are placed on the degree of dependence and the moments of the distributions.


title: Normal distribution

text: Many test statistics, scores, and estimators encountered in practice contain sums of certain random variables in them, and even more estimators can be represented as sums of random variables through the use of influence functions. The central limit theorem implies that those statistical parameters will have asymptotically normal distributions.


title: Normal distribution

text: The central limit theorem also implies that certain distributions can be approximated by the normal distribution, for example:


title: Normal distribution

text: Whether these approximations are sufficiently accurate depends on the purpose for which they are needed, and the rate of convergence to the normal distribution. It is typically the case that such approximations are less accurate in the tails of the distribution.


title: Normal distribution

text: A general upper bound for the approximation error in the central limit theorem is given by the Berry–Esseen theorem, improvements of the approximation are given by the Edgeworth expansions.


title: Normal distribution

text: This theorem can also be used to justify modeling the sum of many uniform noise sources as Gaussian noise. See AWGN.


title: Normal distribution

text: The probability density, cumulative distribution, and inverse cumulative distribution of any function of one or more independent or correlated normal variables can be computed with the numerical method of ray-tracing (Matlab code). In the following sections we look at some special cases.


title: Normal distribution

text: If formula_288 and formula_289 are two independent standard normal random variables with mean 0 and variance 1, then


title: Normal distribution

text: The split normal distribution is most directly defined in terms of joining scaled sections of the density functions of different normal distributions and rescaling the density to integrate to one. The truncated normal distribution results from rescaling a section of a single density function.


title: Normal distribution

text: For any positive integer formula_335, any normal distribution with mean formula_336 and variance formula_6 is the distribution of the sum of formula_335 independent normal deviates, each with mean formula_339 and variance formula_340. This property is called infinite divisibility.


title: Normal distribution

text: Conversely, if formula_288 and formula_289 are independent random variables and their sum formula_343 has a normal distribution, then both formula_288 and formula_289 must be normal deviates.


title: Normal distribution

text: This result is known as Cramér's decomposition theorem, and is equivalent to saying that the convolution of two distributions is normal if and only if both are normal. Cramér's theorem implies that a linear combination of independent non-Gaussian variables will never have an exactly normal distribution, although it may approach it arbitrarily closely.


title: Normal distribution

text: Bernstein's theorem states that if formula_43 and formula_298 are independent and formula_300 and formula_301 are also independent, then both "X" and "Y" must necessarily have normal distributions.


title: Normal distribution

text: More generally, if formula_350 are independent random variables, then two distinct linear combinations formula_351 and formula_352will be independent if and only if all formula_353 are normal and formula_354, where formula_355 denotes the variance of formula_353.


title: Normal distribution

text: The notion of normal distribution, being one of the most important distributions in probability theory, has been extended far beyond the standard framework of the univariate (that is one-dimensional) case (Case 1). All these extensions are also called "normal" or "Gaussian" laws, so a certain ambiguity in names exists.


title: Normal distribution

text: where "μ" is the mean and "σ" and "σ" are the standard deviations of the distribution to the left and right of the mean respectively.


title: Normal distribution

text: One of the main practical uses of the Gaussian law is to model the empirical distributions of many different random variables encountered in practice. In such case a possible extension would be a richer family of distributions, having more than two parameters and therefore being able to fit the empirical distribution more accurately. The examples of such extensions are:


title: Normal distribution

text: It is often the case that we do not know the parameters of the normal distribution, but instead want to estimate them. That is, having a sample formula_362 from a normal formula_363 population we would like to learn the approximate values of parameters formula_3 and formula_6. The standard approach to this problem is the maximum likelihood method, which requires maximization of the "log-likelihood function":


title: Normal distribution

text: Taking derivatives with respect to formula_3 and formula_6 and solving the resulting system of first order conditions yields the "maximum likelihood estimates":


title: Normal distribution

text: Estimator formula_370 is called the "sample mean", since it is the arithmetic mean of all observations. The statistic formula_371 is complete and sufficient for formula_3, and therefore by the Lehmann–Scheffé theorem, formula_370 is the uniformly minimum variance unbiased (UMVU) estimator. In finite samples it is distributed normally:


title: Normal distribution

text: The variance of this estimator is equal to the "μμ"-element of the inverse Fisher information matrix formula_375. This implies that the estimator is finite-sample efficient. Of practical importance is the fact that the standard error of formula_370 is proportional to formula_377, that is, if one wishes to decrease the standard error by a factor of 10, one must increase the number of points in the sample by a factor of 100. This fact is widely used in determining sample sizes for opinion polls and the number of trials in Monte Carlo simulations.


title: Normal distribution

text: From the standpoint of the asymptotic theory, formula_370 is consistent, that is, it converges in probability to formula_3 as formula_380. The estimator is also asymptotically normal, which is a simple corollary of the fact that it is normal in finite samples:


title: Normal distribution

text: The estimator formula_382 is called the "sample variance", since it is the variance of the sample (formula_362). In practice, another estimator is often used instead of the formula_382. This other estimator is denoted formula_385, and is also called the "sample variance", which represents a certain ambiguity in terminology; its square root formula_386 is called the "sample standard deviation". The estimator formula_385 differs from formula_382 by having instead of "n" in the denominator (the so-called Bessel's correction):


title: Normal distribution

text: The difference between formula_385 and formula_382 becomes negligibly small for large "n"s. In finite samples however, the motivation behind the use of formula_385 is that it is an unbiased estimator of the underlying parameter formula_6, whereas formula_382 is biased. Also, by the Lehmann–Scheffé theorem the estimator formula_385 is uniformly minimum variance unbiased (UMVU), which makes it the "best" estimator among all unbiased ones. However it can be shown that the biased estimator formula_382 is "better" than the formula_385 in terms of the mean squared error (MSE) criterion. In finite samples both formula_385 and formula_382 have scaled chi-squared distribution with degrees of freedom:


title: Normal distribution

text: The first of these expressions shows that the variance of formula_385 is equal to formula_402, which is slightly greater than the "σσ"-element of the inverse Fisher information matrix formula_375. Thus, formula_385 is not an efficient estimator for formula_6, and moreover, since formula_385 is UMVU, we can conclude that the finite-sample efficient estimator for formula_6 does not exist.


title: Normal distribution

text: Applying the asymptotic theory, both estimators formula_385 and formula_382 are consistent, that is they converge in probability to formula_6 as the sample size formula_380. The two estimators are also both asymptotically normal:


title: Normal distribution

text: By Cochran's theorem, for normal distributions the sample mean formula_370 and the sample variance "s" are independent, which means there can be no gain in considering their joint distribution. There is also a converse theorem: if in a sample the sample mean and sample variance are independent, then the sample must have come from the normal distribution. The independence between formula_370 and "s" can be employed to construct the so-called "t-statistic":


title: Normal distribution

text: This quantity "t" has the Student's t-distribution with degrees of freedom, and it is an ancillary statistic (independent of the value of the parameters). Inverting the distribution of this "t"-statistics will allow us to construct the confidence interval for "μ"; similarly, inverting the "χ" distribution of the statistic "s" will give us the confidence interval for "σ":


title: Normal distribution

text: where "t" and are the "p"th quantiles of the "t"- and "χ"-distributions respectively. These confidence intervals are of the "confidence level" , meaning that the true values "μ" and "σ" fall outside of these intervals with probability (or significance level) "α". In practice people usually take , resulting in the 95% confidence intervals.


title: Normal distribution

text: The approximate formulas become valid for large values of "n", and are more convenient for the manual calculation since the standard normal quantiles "z" do not depend on "n". In particular, the most popular value of , results in .


title: Normal distribution

text: Normality tests assess the likelihood that the given data set {"x", ..., "x"} comes from a normal distribution. Typically the null hypothesis "H" is that the observations are distributed normally with unspecified mean "μ" and variance "σ", versus the alternative "H" that the distribution is arbitrary. Many tests (over 40) have been devised for this problem. The more prominent of them are outlined below:


title: Normal distribution

text: Diagnostic plots are more intuitively appealing but subjective at the same time, as they rely on informal human judgement to accept or reject the null hypothesis.


title: Normal distribution

text: Bayesian analysis of normally distributed data is complicated by the many different possibilities that may be considered:


title: Normal distribution

text: The following auxiliary formula is useful for simplifying the posterior update equations, which otherwise become fairly tedious.


title: Normal distribution

text: This equation rewrites the sum of two quadratics in "x" by expanding the squares, grouping the terms in "x", and completing the square. Note the following about the complex constant factors attached to some of the terms:


title: Normal distribution

text: A similar formula can be written for the sum of two vector quadratics: If x, y, z are vectors of length "k", and A and B are symmetric, invertible matrices of size formula_427, then


title: Normal distribution

text: In other words, it sums up all possible combinations of products of pairs of elements from x, with a separate coefficient for each. In addition, since formula_431, only the sum formula_432 matters for any off-diagonal elements of A, and there is no loss of generality in assuming that A is symmetric. Furthermore, if A is symmetric, then the form formula_433


title: Normal distribution

text: For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with known variance σ, the conjugate prior distribution is also normally distributed.


title: Normal distribution

text: This can be shown more easily by rewriting the variance as the precision, i.e. using τ = 1/σ. Then if formula_437 and formula_438 we proceed as follows.


title: Normal distribution

text: First, the likelihood function is (using the formula above for the sum of differences from the mean):


title: Normal distribution

text: In the above derivation, we used the formula above for the sum of two quadratics and eliminated all constant factors not involving "μ". The result is the kernel of a normal distribution, with mean formula_441 and precision formula_442, i.e.


title: Normal distribution

text: This can be written as a set of Bayesian update equations for the posterior parameters in terms of the prior parameters:


title: Normal distribution

text: That is, to combine "n" data points with total precision of "nτ" (or equivalently, total variance of "n"/"σ") and mean of values formula_445, derive a new total precision simply by adding the total precision of the data to the prior total precision, and form a new mean through a "precision-weighted average", i.e. a weighted average of the data mean and the prior mean, each weighted by the associated total precision. This makes logical sense if the precision is thought of as indicating the certainty of the observations: In the distribution of the posterior mean, each of the input components is weighted by its certainty, and the certainty of this distribution is the sum of the individual certainties. (For the intuition of this, compare the expression "the whole is (or is not) greater than the sum of its parts". In addition, consider that the knowledge of the posterior comes from a combination of the knowledge of the prior and likelihood, so it makes sense that we are more certain of it than of either of its components.)


title: Normal distribution

text: The above formula reveals why it is more convenient to do Bayesian analysis of conjugate priors for the normal distribution in terms of the precision. The posterior precision is simply the sum of the prior and likelihood precisions, and the posterior mean is computed through a precision-weighted average, as described above. The same formulas can be written in terms of variance by reciprocating all the precisions, yielding the more ugly formulas


title: Normal distribution

text: For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with known mean μ, the conjugate prior of the variance has an inverse gamma distribution or a scaled inverse chi-squared distribution. The two are equivalent except for having different parameterizations. Although the inverse gamma is more commonly used, we use the scaled inverse chi-squared for the sake of convenience. The prior for σ is as follows:


title: Normal distribution

text: For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with unknown mean μ and unknown variance σ, a combined (multivariate) conjugate prior is placed over the mean and variance, consisting of a normal-inverse-gamma distribution.


title: Normal distribution

text: The respective numbers of pseudo-observations add the number of actual observations to them. The new mean hyperparameter is once again a weighted average, this time weighted by the relative numbers of observations. Finally, the update for formula_458 is similar to the case with known mean, but in this case the sum of squared deviations is taken with respect to the observed data mean rather than the true mean, and as a result a new "interaction term" needs to be added to take care of the additional error source stemming from the deviation between prior and data mean.


title: Normal distribution

text: &= \frac{(\sigma_0^2\nu_0/2)^{\nu_0/2}}{\Gamma(\nu_0/2)}~\frac{\exp\left[ \frac{-\nu_0 \sigma_0^2}{2 \sigma^2}\right]}{(\sigma^2)^{1+\nu_0/2}} \\


title: Normal distribution

text: In other words, the posterior distribution has the form of a product of a normal distribution over "p"("μ" | "σ") times an inverse gamma distribution over "p"(σ), with parameters that are the same as the update equations above.


title: Normal distribution

text: The occurrence of normal distribution in practical problems can be loosely classified into four categories:


title: Normal distribution

text: Certain quantities in physics are distributed normally, as was first demonstrated by James Clerk Maxwell. Examples of such quantities are:


title: Normal distribution

text: "Approximately" normal distributions occur in many situations, as explained by the central limit theorem. When the outcome is produced by many small effects acting "additively and independently", its distribution will be close to normal. The normal approximation will not be valid if the effects act multiplicatively (instead of additively), or if there is a single external influence that has a considerably larger magnitude than the rest of the effects.


title: Normal distribution

text: There are statistical methods to empirically test that assumption; see the above Normality tests section.


title: Normal distribution

text: John Ioannidis argues that using normally distributed standard deviations as standards for validating research findings leave falsifiable predictions about phenomena that are not normally distributed untested. This includes, for example, phenomena that only appear when all necessary conditions are present and one cannot be a substitute for another in an addition-like way and phenomena that are not randomly distributed. Ioannidis argues that standard deviation-centered validation gives a false appearance of validity to hypotheses and theories where some but not all falsifiable predictions are normally distributed since the portion of falsifiable predictions that there is evidence against may and in some cases are in the non-normally distributed parts of the range of falsifiable predictions, as well as baselessly dismissing hypotheses for which none of the falsifiable predictions are normally distributed as if were they unfalsifiable when in fact they do make falsifiable predictions. It is argued by Ioannidis that many cases of mutually exclusive theories being accepted as "validated" by research journals are caused by failure of the journals to take in empirical falsifications of non-normally distributed predictions, and not because mutually exclusive theories are true, which they cannot be, although two mutually exclusive theories can both be wrong and a third one correct.


title: Normal distribution

text: In computer simulations, especially in applications of the Monte-Carlo method, it is often desirable to generate values that are normally distributed. The algorithms listed below all generate the standard normal deviates, since a can be generated as , where "Z" is standard normal. All these algorithms rely on the availability of a random number generator "U" capable of producing uniform random variates.


title: Normal distribution

text: The values Φ("x") may be approximated very accurately by a variety of methods, such as numerical integration, Taylor series, asymptotic series and continued fractions. Different approximations are used depending on the desired level of accuracy.


title: Normal distribution

text: Shore (1982) introduced simple approximations that may be incorporated in stochastic optimization models of engineering and operations research, like reliability engineering and inventory analysis. Denoting , the simplest approximation for the quantile function is:


title: Normal distribution

text: This approximation delivers for "z" a maximum absolute error of 0.026 (for , corresponding to ). For replace "p" by and change sign. Another approximation, somewhat less accurate, is the single-parameter approximation:


title: Normal distribution

text: The latter had served to derive a simple approximation for the loss integral of the normal distribution, defined by


title: Normal distribution

text: This approximation is particularly accurate for the right far-tail (maximum error of 10 for z≥1.4). Highly accurate approximations for the CDF, based on Response Modeling Methodology (RMM, Shore, 2011, 2012), are shown in Shore (2005).


title: Normal distribution

text: Some more approximations can be found at: Error function#Approximation with elementary functions. In particular, small "relative" error on the whole domain for the CDF formula_68 and the quantile function formula_474 as well, is achieved via an explicitly invertible formula by Sergei Winitzki in 2008.


title: Normal distribution

text: Some authors attribute the credit for the discovery of the normal distribution to de Moivre, who in 1738 published in the second edition of his ""The Doctrine of Chances"" the study of the coefficients in the binomial expansion of . De Moivre proved that the middle term in this expansion has the approximate magnitude of formula_475, and that "If "m" or "n" be a Quantity infinitely great, then the Logarithm of the Ratio, which a Term distant from the middle by the Interval "ℓ", has to the middle Term, is formula_476." Although this theorem can be interpreted as the first obscure expression for the normal probability law, Stigler points out that de Moivre himself did not interpret his results as anything more than the approximate rule for the binomial coefficients, and in particular de Moivre lacked the concept of the probability density function.


title: Normal distribution

text: In 1823 Gauss published his monograph ""Theoria combinationis observationum erroribus minimis obnoxiae"" where among other things he introduces several important statistical concepts, such as the method of least squares, the method of maximum likelihood, and the "normal distribution". Gauss used "M", , to denote the measurements of some unknown quantity "V", and sought the "most probable" estimator of that quantity: the one that maximizes the probability of obtaining the observed experimental results. In his notation φΔ is the probability density function of the measurement errors of magnitude Δ. Not knowing what the function "φ" is, Gauss requires that his method should reduce to the well-known answer: the arithmetic mean of the measured values. Starting from these principles, Gauss demonstrates that the only law that rationalizes the choice of arithmetic mean as an estimator of the location parameter, is the normal law of errors:


title: Normal distribution

text: where "h" is "the measure of the precision of the observations". Using this normal law as a generic model for errors in the experiments, Gauss formulates what is now known as the non-linear weighted least squares method.


title: Normal distribution

text: Although Gauss was the first to suggest the normal distribution law, Laplace made significant contributions. It was Laplace who first posed the problem of aggregating several observations in 1774, although his own solution led to the Laplacian distribution. It was Laplace who first calculated the value of the integral in 1782, providing the normalization constant for the normal distribution. Finally, it was Laplace who in 1810 proved and presented to the Academy the fundamental central limit theorem, which emphasized the theoretical importance of the normal distribution.


title: Normal distribution

text: It is of interest to note that in 1809 an Irish-American mathematician Robert Adrain published two insightful but flawed derivations of the normal probability law, simultaneously and independently from Gauss. His works remained largely unnoticed by the scientific community, until in 1871 they were exhumed by Abbe.


title: Normal distribution

text: In the middle of the 19th century Maxwell demonstrated that the normal distribution is not just a convenient mathematical tool, but may also occur in natural phenomena: "The number of particles whose velocity, resolved in a certain direction, lies between "x" and "x" + "dx" is


title: Normal distribution

text: Today, the concept is usually known in English as the normal distribution or Gaussian distribution. Other less common names include Gauss distribution, Laplace-Gauss distribution, the law of error, the law of facility of errors, Laplace's second law, Gaussian law.


title: Normal distribution

text: Gauss himself apparently coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual". However, by the end of the 19th century some authors had started using the name "normal distribution", where the word "normal" was used as an adjective – the term now being seen as a reflection of the fact that this distribution was seen as typical, common – and thus "normal". Peirce (one of those authors) once defined "normal" thus: "...the 'normal' is not the average (or any other kind of mean) of what actually occurs, but of what "would", in the long run, occur under certain circumstances." Around the turn of the 20th century Pearson popularized the term "normal" as a designation for this distribution.


title: Normal distribution

text: Also, it was Pearson who first wrote the distribution in terms of the standard deviation "σ" as in modern notation. Soon after this, in year 1915, Fisher added the location parameter to the formula for normal distribution, expressing it in the way it is written nowadays:


title: Normal distribution

text: The term "standard normal", which denotes the normal distribution with zero mean and unit variance came into general use around the 1950s, appearing in the popular textbooks by P. G. Hoel (1947) ""Introduction to mathematical statistics"" and A. M. Mood (1950) ""Introduction to the theory of statistics"".


title: Christopher Reeve

text: Christopher D'Olier Reeve (September 25, 1952 – October 10, 2004) was an American actor, best known for playing the title character in the film "Superman" (1978) and three sequels.


title: Christopher Reeve

text: Born in New York City and raised in Princeton, New Jersey, Reeve discovered a passion for acting and the theater at the age of nine. He studied at Cornell University and the Juilliard School and made his Broadway debut in 1976. After his acclaimed performances in "Superman" and "Superman II", Reeve declined many roles in action movies, choosing instead to work in small films and plays with more complex characters. He later appeared in critically successful films such as "The Bostonians" (1984), "Street Smart" (1987), and "The Remains of the Day" (1993), and in the plays "Fifth of July" on Broadway and "The Aspern Papers" in London's West End.


title: Christopher Reeve

text: On May 27, 1995, Reeve broke his neck when he was thrown from a horse during an equestrian competition in Culpeper, Virginia. The injury paralyzed him from the shoulders down, and he used a wheelchair and ventilator for the rest of his life. Reeve returned to creative work, directing "In the Gloaming" (1997) and acting in the television remake of "Rear Window" (1998). He also made several appearances in the Superman-themed television series "Smallville", and wrote two autobiographical books, "Still Me" and "Nothing is Impossible". Over the course of his career, Reeve received a BAFTA Award, a Screen Actors Guild Award, an Emmy Award, and a Grammy Award.


title: Christopher Reeve

text: Beginning in the 1980s, Reeve was an activist for environmental and human-rights causes and for artistic freedom of expression. After his accident, he lobbied for spinal injury research, including human embryonic stem cell research, and for better insurance coverage for people with disabilities. His advocacy work included leading the Christopher and Dana Reeve Foundation and co-founding the Reeve-Irvine Research Center. Reeve died on October 10, 2004.


title: Christopher Reeve

text: Reeve was born on September 25, 1952, in New York City, the son of Barbara Pitney Lamb, a journalist; and Franklin D'Olier Reeve (1928–2013), a teacher, novelist, poet, and scholar. Many of his ancestors had been in America since the early 17th century, some having been aboard the Mayflower. Other ancestors of Reeve came from the French aristocracy. His paternal grandfather, Colonel Richard Henry Reeve, had been the CEO of Prudential Financial (when it was called Prudential Life Insurance Company) for over 25 years.


title: Christopher Reeve

text: Franklin and Barbara divorced in 1956, and she moved with Christopher and his younger brother to Princeton, New Jersey, where they attended Nassau Street School and then Princeton Country Day School (today called the Princeton Day School). Reeve's parents both remarried. Reeve excelled academically, athletically, and onstage; he was on the honor roll and played soccer, baseball, tennis, and hockey. The sportsmanship award at Princeton Day School's invitational hockey tournament was named in Reeve's honor.


title: Christopher Reeve

text: Reeve had a difficult relationship with his father, Franklin. He wrote in 1998 that his father's "love for his children always seemed tied to performance" and he put pressure on himself to act older than he actually was in order to gain his father's approval. Between 1988 and 1995 the two barely spoke to each other, but they reconciled after Reeve's paralyzing accident.


title: Christopher Reeve

text: Reeve found his passion for acting in 1962 at age nine when he was cast in an amateur version of the operetta "The Yeomen of the Guard"; it was the first of many student plays. His interest was solidified when at age fifteen, he spent a summer as an apprentice at the Williamstown Theatre Festival in Williamstown, Massachusetts.


title: Christopher Reeve

text: After graduating from Princeton Day School in June 1970, Reeve acted in plays in Boothbay, Maine. He planned to go to New York City to find a career in theater. Ultimately, however, at the advice of his mother, he applied for college. He was accepted into Princeton University, Columbia University, Brown University, Cornell University, Northwestern University, and Carnegie Mellon University. Reeve said he chose Cornell primarily because it was distant from New York City and this would help him avoid the temptation of working as an actor immediately versus finishing college, as he had promised his mother and stepfather. Reeve joined the theater department in Cornell and played Pozzo in "Waiting for Godot", Segismundo in "Life Is a Dream", Hamlet in "Rosencrantz and Guildenstern Are Dead", and Polixenes in "The Winter's Tale".


title: Christopher Reeve

text: Late in his freshman year, Reeve received a letter from Stark Hesseltine, a high-powered New York City agent who had discovered Robert Redford and who represented actors such as Richard Chamberlain, Michael Douglas, and Susan Sarandon. Hesseltine had seen Reeve in "A Month in the Country" and wanted to represent him. Reeve was very excited and kept re-reading the letter to make sure of what it said. Reeve was impatient with school and anxious to get on with his career. The two met, but Reeve was surprised to find Hesseltine strongly supported his promise to his mother and stepfather to complete college. They decided instead of dropping out of school, Reeve would come to New York once a month to meet casting agents and producers to find work for the summer vacation.


title: Christopher Reeve

text: Reeve received favorable responses to his introductions and auditions arranged by Hesseltine but had to forgo several desirable opportunities because they began before school ended. In the summer, he toured in a production of "Forty Carats" with Eleanor Parker. The next year, Reeve received a full summer contract with the San Diego Shakespeare Festival, with roles as Edward IV in "Richard III", Fenton in "The Merry Wives of Windsor", and Dumaine in "Love's Labour's Lost" at the Old Globe Theatre.


title: Christopher Reeve

text: Before his third year of college, Reeve took a three-month leave of absence. He traveled to Glasgow, Scotland, and saw theatrical productions throughout the United Kingdom. He was inspired by the actors there, and often had conversations with them in bars after their performances. He helped actors at the Old Vic with their American accents by reading the newspaper aloud for them. He then flew to Paris to study the French theater. Reeve spoke fluent French, having studied it from the third grade through his first year in Cornell. While there he spoke only French to immerse himself in French culture, and watched many performances before returning to New York to reunite with his girlfriend.


title: Christopher Reeve

text: After returning to the US from Europe, Reeve chose to focus solely on acting, although Cornell had several general education requirements for graduation he had yet to complete. He managed to convince theater director Jim Clause and the dean of the College of Arts and Sciences, as a theater major, he would achieve more at Juilliard (Group 4, 1973–1975) in New York City than at Cornell. They agreed his first year at Juilliard would be counted as his senior year at Cornell.


title: Christopher Reeve

text: In 1973, approximately 2,000 students auditioned for 20 places in the freshman class at Juilliard. Reeve's audition was in front of 10 faculty members, including John Houseman, who had just won an Academy Award for "The Paper Chase". Reeve and Robin Williams were the only students selected for Juilliard's Advanced Program. They had several classes together in which they were the only students. In their dialects class with Edith Skinner, Williams had no trouble mastering all dialects naturally, whereas Reeve was more meticulous about it. Williams and Reeve developed a close friendship.


title: Christopher Reeve

text: In a meeting with Houseman, Reeve was told, "Mr. Reeve. It is terribly important that you become a serious classical actor. Unless, of course, they offer you a shitload of money to do something else." Houseman then offered him the chance to leave school and join the Acting Company, among performers such as Kevin Kline, Patti LuPone, and David Ogden Stiers. Reeve declined, as he had not yet received his bachelor's degree.


title: Christopher Reeve

text: In early 1974, Reeve and other Juilliard students toured the New York City junior high school system and performed "The Love Cure". In one performance, Reeve, who played the hero, drew his sword out too high and accidentally destroyed a row of lights above him. The students applauded and cheered. Reeve later said this was the greatest ovation of his career. After completing his first year at Juilliard, Reeve graduated from Cornell in the Class of 1974 with a Bachelor of Arts degree.


title: Christopher Reeve

text: In late 1975, Reeve auditioned for the Broadway play "A Matter of Gravity". Katharine Hepburn watched his audition and cast him as her character's grandson in the play. With Hepburn's influence over the CBS network, Reeve worked out the schedules of the soap opera "Love of Life" and the play so he would be able to do both. Because of his busy schedule, he ate candy bars and drank coffee in place of meals and experienced exhaustion and malnutrition. On the first night of the play's run, Reeve entered the stage, said his first line, and then promptly fainted. Hepburn turned to the audience and said, "This boy's a goddamn fool. He doesn't eat enough red meat." The understudy finished the play for Reeve, and a doctor treated him. The doctor advised Reeve to eat a healthier diet. He stayed with the play throughout its year-long run and was given very favorable reviews.


title: Christopher Reeve

text: Reeve and Hepburn became very close. She said, "You're going to be a big star, Christopher, and support me in my old age." He replied, "I can't wait long." Some gossip columns rumored a romance between the two. Reeve said, "She was 67 and I was 22, but I thought that was quite an honor ... I believe I was fairly close to what a child or grandchild might have been to her." Reeve said his father, who was a professor of literature and came to many of the performances, was the man who most captivated Hepburn. When the play moved to Los Angeles in 1976, Reeve—to Hepburn's disappointment—dropped out. They stayed in touch for years after the play's run. Reeve later regretted not staying closer and just sending messages back and forth.


title: Christopher Reeve

text: Reeve's first role in a Hollywood film was a very small part as a junior officer in the 1978 naval submarine disaster movie "Gray Lady Down", starring Charlton Heston. He then acted in the play "My Life" at the Circle Repertory Company with friend William Hurt.


title: Christopher Reeve

text: During "My Life", Stark Hesseltine told Reeve he had been asked to audition for the leading role as Clark Kent/Superman in the big budget film "Superman" (1978). Lynn Stalmaster, the casting director, put Reeve's picture and résumé on the top of the pile three separate times, only to have the producers throw it out each time. Through Stalmaster's persistent pleading, a meeting between director Richard Donner, producer Ilya Salkind, and Reeve was arranged. The morning after the meeting, Reeve was sent a 300-page script. He was thrilled the script took the subject matter seriously, and Donner's motto was "verisimilitude". Reeve flew to London for a screen test, and on the way was told Marlon Brando was going to play Jor-El and Gene Hackman was going to play Lex Luthor. Reeve still did not think he had much of a chance. On the plane ride to London, he imagined how his approach to the role would be. He later said, "By the late 1970s, the masculine image had changed ... Now it was acceptable for a man to show gentleness and vulnerability. I felt that the new Superman ought to reflect that contemporary male image." He based his portrayal of Clark Kent on Cary Grant in his role in "Bringing Up Baby". After the screen test, his driver said, "I'm not supposed to tell you this, but you've got the part."


title: Christopher Reeve

text: Portraying Superman would be a stretch for the 24-year-old actor. He was tall, but his physique was slim. Reeve went through an intense two-month training regimen with former British weightlifting champion David Prowse supervising. The training regimen consisted of running in the morning, followed by two hours of weightlifting and 90 minutes on the trampoline. He added of muscle to his "thin" frame. He later made even higher gains for "Superman III" (1983), though for "" (1987), he decided it would be healthier to focus more on cardiovascular workouts. One of the reasons Reeve could not work out as much for "Superman IV" was an emergency appendectomy he had in June 1986.


title: Christopher Reeve

text: Reeve was never a Superman or comic book fan, though he had watched "Adventures of Superman" starring George Reeves. Reeve found the role offered a suitable challenge because it was a dual role. He said, "there must be some difference stylistically between Clark and Superman. Otherwise, you just have a pair of glasses standing in for a character."


title: Christopher Reeve

text: On the commentary track for the director's edition of "", creative consultant Tom Mankiewicz spoke of how Reeve had talked to him about playing Superman and then playing Clark Kent. Mankiewicz then corrected Reeve, telling him he was "always, "always" playing Superman" and when he was Clark Kent, he was "playing Superman who was playing Clark Kent." Mankiewicz described it to Reeve as a role within a role.


title: Christopher Reeve

text: The film, made without the use of computers for special effects, was the first attempt to realistically show a person flying. Roy Field, the film's optical supervisor, said, "There were many techniques used to make Superman fly, but the best special effect of all was Christopher Reeve himself. We discovered very early on he, being a glider pilot, could hold his body aerodynamically. So when he got into the harness, the whole shot began to come alive."


title: Christopher Reeve

text: The film grossed $300.2 million worldwide (unadjusted for inflation). Reeve received positive reviews for his performance:


title: Christopher Reeve

text: For his performance, Reeve won a BAFTA Award for Most Promising Newcomer to Leading Film Roles. Reeve described Superman as "the closest opportunity I've had to playing a classical role on film, the closest expression to something of mythical dimension." His co-star Margot Kidder said after his death with the "Superman" films, Reeve "knew he'd done something meaningful. He was very aware of that and very happy with that role."


title: Christopher Reeve

text: Reeve used his celebrity status for several philanthropic causes. Through the Make-A-Wish Foundation, he visited terminally ill children. He joined the board of directors for the worldwide charity Save the Children. In 1979, he served as a track and field coach at the Special Olympics alongside O. J. Simpson.


title: Christopher Reeve

text: Much of "Superman II" was filmed at the same time as the first film. In fact, the original plan had been for the film to be a single three-hour epic comprising both parts. After most of the footage had been shot, the producers had a disagreement with director Richard Donner over various matters, including money and special effects, and they mutually agreed to part ways. Director Richard Lester, who had worked with the producers previously on the two-parter "The Three Musketeers" (1973) and "The Four Musketeers" (1974), replaced Donner. Lester had the script changed and re-shot some footage. The cast was unhappy, but Reeve later said he liked Lester and considered "Superman II" to be his favorite of the series. Richard Donner's version of "Superman II", titled "", was released on DVD in November 2006 and was dedicated in memory of Reeve.


title: Christopher Reeve

text: Lester directed "Superman III", released in 1983, solo. Reeve believed the producers Alexander Salkind, his son Ilya Salkind, and Pierre Spengler decreased the credibility of "Superman III" by turning it into a Richard Pryor comedy, hence making it a not very good film. He missed Donner and believed "Superman III" only really good element was the automobile junkyard scene in which Evil Superman fights Good Clark Kent in an internal battle. Reeve's portrayal of the Evil Superman was highly praised, though the film was critically panned. Any negative review for "Superman III", however, was nothing compared to the totally negative reception its successor would receive.


title: Christopher Reeve

text: "" was released in 1987. After "Superman III", Reeve vowed he was done with Superman. However, he agreed to continue the role in a fourth film on the condition he would have partial creative control over the script. The nuclear disarmament plot was his idea. Cannon Films purchased the production rights to the character of Superman from Alexander Salkind and his son Ilya Salkind, the original producers of the film series, in the mid-1980s. Cannon Films were known for low-budget, poorly-acted, poorly-scripted action films. They cut the budget of "Superman IV" in half to $17 million. The film was both a critical failure and a box-office disappointment, becoming the lowest-grossing Superman film to date. Reeve later said, "the less said about "Superman IV" the better." Both of Reeve's children from his relationship with Gae Exton had uncredited appearances in a deleted scene in which Superman rescues a girl, played by his daughter Alexandra, and reunites her with her brother, played by his son Matthew, after Nuclear Man creates a tornado in Smallville.


title: Christopher Reeve

text: Reeve would have made a fifth Superman film after the rights to the character reverted to Alexander Salkind, Ilya Salkind, and Pierre Spengler if the film had a budget the same size as of "Superman: The Movie". Although there was potential for such a film in the late 1980s after Cannon Films went bankrupt, Reeve never received any script.


title: Christopher Reeve

text: In 1993, two years before Reeve's accident, the Salkinds sold the rights to the character of Superman again, this time to Warner Bros. "There was supposed to be a fifth Superman movie titled "Superman Reborn", but because of studio shifts, the terrible box office ["Superman IV"] got, and ... Reeves's accident, it never saw the light of day."


title: Christopher Reeve

text: Reeve's first role after 1978's "Superman" was in the 1980 time-travel mystery/romantic fantasy "Somewhere in Time". Reeve as Richard Collier romanced actress Elise McKenna, a popular stage actress from the early 20th century, played by Jane Seymour. The film was shot on Mackinac Island using the Grand Hotel in mid-1979, and was Reeve's favorite film to shoot.


title: Christopher Reeve

text: After the film was completed, the plan was for a limited release and to build word of mouth, but early test screenings were favorable and the studio decided on a wide release, which proved to be the wrong strategy. Early reviews savaged the film as unduly sentimental and melodramatic, and an actors' strike prevented Reeve and Seymour from doing publicity. The film quickly closed, although Jean-Pierre Dorléac was nominated for an Academy Award for Best Costume Design in 1980. The film, commercially unsuccessful, was Reeve's first public disappointment. However, almost ten years after "Somewhere in Time" was released, at a time when other period films were beginning to be made, it became a cult film favorite, thanks to screenings on cable networks and video rentals; its popularity began to grow, vindicating the belief of the creative team. INSITE, the International Network of "Somewhere in Time" Enthusiasts, did fundraising to sponsor a star on the Hollywood Walk of Fame in 1997 for Reeve. Jane Seymour became a friend of Reeve and in 1996 named one of her twin sons Kristopher in his honor. The Grand Hotel and Mackinac Island has become a popular tourist site for film fans.


title: Christopher Reeve

text: In that same year, Reeve made a guest appearance on "The Muppet Show", where he performed "East of the Sun (and West of the Moon)" on a piano for Miss Piggy, who had a crush on him. Reeve denied being Superman but displayed the character's superpowers throughout the episode. He then returned to continue filming on the not yet finished production of "Superman II".


title: Christopher Reeve

text: After finishing "Superman II", Reeve and his family left London and rented a house in the Hollywood Hills. Soon after, Reeve grew tired of Hollywood and took the family to Williamstown, Massachusetts, where he played the lead in the successful play "The Front Page", directed by Robert Allan Ackerman. Later in the year, Reeve played a disabled Vietnam veteran in Lanford Wilson's play "Fifth of July" on Broadway to excellent reviews. To prepare for the role, he was coached by an amputee on how to walk on artificial legs.


title: Christopher Reeve

text: In 1982 Reeve stretched his acting range further and played a devious novice playwright with questionable motives regarding his lover and mentor Michael Caine, in Sidney Lumet's suspenseful dark comedy film "Deathtrap", based on the play by Ira Levin. The film was well received. The same year, Reeve portrayed corrupt Catholic priest John Flaherty making challenging decisions during World War II in "Monsignor". Reeve felt this gave him the opportunity to play "a morally ambiguous character who was neither clearly good nor clearly bad, someone to whom life is much more complex than the characters I've played previously". Reeve blamed the failure of the film on poor editing. He said "the movie is sort of a series of outrageous incidents that you find hard to believe. Since they don't have a focus, and since they aren't justified and explained, they become laughable".


title: Christopher Reeve

text: Reeve was then offered the role of Basil Ransom in 1984's "The Bostonians" alongside Vanessa Redgrave. Though Reeve ordinarily commanded over one million dollars per film, the producers could only afford to pay him one-tenth of that. Reeve had no complaints, as he was happy to be doing a role of which he could be proud. The film exceeded expectations and performed well at the box office for what was considered to be an art house film. "The New York Times" called it "the best adaptation of a literary work yet made for the screen." Katharine Hepburn called Reeve to tell him he was "absolutely marvelous" and "captivating" in the film. When he told her he was currently shooting the 1985 version of "Anna Karenina", she said, "Oh, that's a terrible mistake."


title: Christopher Reeve

text: Reeve was a licensed pilot and flew solo across the Atlantic twice. During the filming of "Superman III", he raced his sailplane in his free time. He joined The Tiger Club, a group of aviators who had served in the Royal Air Force in the Battle of Britain. They let him participate in mock dogfights in vintage World War I combat planes. The producers of the film "The Aviator" approached him without knowing he was a pilot and he knew how to fly a Stearman, the plane used in the film. Reeve readily accepted the role. The film was shot in Kranjska Gora, and Reeve performed all his own stunts.


title: Christopher Reeve

text: In 1984, Reeve appeared in "The Aspern Papers" with Vanessa Redgrave. He then played Tony in "The Royal Family" and the Count in a modern adaptation of the play "The Marriage of Figaro".


title: Christopher Reeve

text: In 1985, Reeve hosted the television documentary "Dinosaur!" Fascinated with dinosaurs since he was a child, as he says in the documentary, he flew himself to New York in his own plane to shoot on location at the American Museum of Natural History. Also, in 1985, DC Comics named Reeve as one of the honorees in the company's 50th-anniversary publication "Fifty Who Made DC Great" for his work on the Superman film series.


title: Christopher Reeve

text: In 1986, he was still struggling to find scripts he liked. A script named "Street Smart" had been lying in his house for years, and after re-reading it, he had Cannon Films green-light it. He starred opposite Morgan Freeman, who was nominated for his first Academy Award for the film. The film received excellent reviews but performed poorly at the box office, possibly because Cannon Films had failed to properly advertise it.


title: Christopher Reeve

text: After the filming of "Superman IV" in February 1987, Reeve and Exton separated and Reeve returned to New York. In June, he appeared in the British television special charity event "The Grand Knockout Tournament". In a depression without his children, aged seven and three, he decided doing a comedy might be good for him. He was given a lead in "Switching Channels". Burt Reynolds and Kathleen Turner had a feud during filming, which made the time even more unbearable for Reeve. Reeve later stated he made a fool of himself in the film and most of his time was spent refereeing between Reynolds and Turner. The film did poorly, and Reeve believed it marked the end of his movie star career. He spent the next years mostly doing plays. He auditioned for the Richard Gere role in "Pretty Woman" but walked out on the audition because they had a half-hearted casting director fill in for Julia Roberts.


title: Christopher Reeve

text: In the late 1980s, Reeve became more active. He was taking horse-riding lessons and trained five to six days a week for competition in combined training events. He built a sailboat, "The Sea Angel", and sailed from the Chesapeake to Nova Scotia.


title: Christopher Reeve

text: In 1990, Reeve starred in the American Civil War film "The Rose and the Jackal", in which he played Allan Pinkerton, the head of President Lincoln's new Secret Service. In October, Reeve was offered the part of Lewis in "The Remains of the Day". The script was one of the best he had read, and he unhesitatingly took the part. The film was deemed an instant classic and was nominated for eight Academy Awards.


title: Christopher Reeve

text: In 1992, Reeve played a lead role in the movie comedy "Noises Off", in which he played a character named Frederick Dallas.


title: Christopher Reeve

text: In the early 1990s, Reeve was in three roles for television in which he was cast as a villain. The most notable of these was "Bump in the Night", in which Reeve played a child molester who abducts a young boy in New York City. The movie received fair to positive reviews. Reeve felt it was important for parents of young children to see the film. In another television movie, "Mortal Sins" (1992), Reeve for the second time played a Catholic priest, this time hearing the confessions of a serial murderer in a role reminiscent of Montgomery Clift in Hitchcock's "I Confess".


title: Christopher Reeve

text: In the 1990s, Reeve received scripts for "Picket Fences" and "Chicago Hope" and was asked by CBS if he wanted to start his own television series. This would have meant moving to Los Angeles, which would place him even further from his children, who lived in London. In Massachusetts, Reeve could take a Concorde and see them at any time. He declined the offers. Reeve did not object to all long-distance journeys; he went to New Mexico to shoot "Speechless", co-starring Michael Keaton. Reeve then went to Point Reyes to shoot John Carpenter's film "Village of the Damned", a remake of a 1960 British movie of the same name. Both of the films with this title were based on the 1957 novel "The Midwich Cuckoos" by John Wyndham.


title: Christopher Reeve

text: Shortly before his accident, Reeve played a paralyzed police officer in the HBO movie "Above Suspicion". He did research at a rehabilitation hospital in Van Nuys and learned how to use a wheelchair to get in and out of cars. His injury occurred less than a week after the premiere of the film.


title: Christopher Reeve

text: In 1995, Reeve was offered the lead in "Kidnapped". He also planned to direct his first big screen film, a romantic comedy entitled "Tell Me True". Both plans were cancelled as a result of the horseback riding accident in 1995 that left him paralyzed.


title: Christopher Reeve

text: In 1996, Reeve narrated the HBO film "". The film won the Emmy Award for "Outstanding Informational Special". He then acted in a small role in the film "A Step Toward Tomorrow".


title: Christopher Reeve

text: In 1997, Reeve made his directorial debut with the HBO film "In the Gloaming" with Robert Sean Leonard, Glenn Close, Whoopi Goldberg, Bridget Fonda, and David Strathairn. The film won four Cable Ace Awards and was nominated for five Emmy Awards including "Outstanding Director for a Miniseries or Special". Dana Reeve said, "There's such a difference in his outlook, his health, his overall sense of well-being when he's working at what he loves, which is creative work." In 1998, Reeve produced and starred in "Rear Window", a remake of Alfred Hitchcock's 1954 film. He was nominated for a Golden Globe and won a Screen Actors Guild Award for his performance.


title: Christopher Reeve

text: On April 25, 1998, Random House published Reeve's autobiography, "Still Me". The book spent eleven weeks on the "New York Times" Best Seller list and Reeve won a Grammy Award for Best Spoken Word Album. In 2000, he made guest appearances on the long-running PBS series "Sesame Street".


title: Christopher Reeve

text: On February 25, 2003, Reeve appeared in the television series "Smallville" as Dr. Virgil Swann in the episode "Rosetta". In the episode, Dr. Swann brings to Clark Kent (Tom Welling) information about where he comes from and how to use his powers for the good of mankind. The scenes of Reeve and Welling feature music cues from 1978's "Superman: The Movie", composed by John Williams and arranged by Mark Snow. At the end of this episode, Reeve and Welling appeared in a short spot inviting people to support the Christopher Reeve Paralysis Foundation. "Rosetta" set ratings history for The WB. The fan community met the episode with rave reviews and praised it as being among the series' best to this day. Reeve also appeared in the "Smallville" episode "Legacy", in which he met again with fellow stage actor John Glover, who played Lionel Luthor in the show.


title: Christopher Reeve

text: In April 2002, Random House published Reeve's second book, "Nothing Is Impossible". This book is shorter than "Still Me" and focuses on Reeve's world views and the life experiences helped him shape them. Also, in 2004, Reeve directed the A&E film "The Brooke Ellison Story". The film is based on the true story of Brooke Ellison, the first quadriplegic to graduate from Harvard University. Reeve during this time was directing the animated film "Everyone's Hero". It was one of his dream projects and he died during the middle of production for the film. His wife Dana helped out, and his son Will was a cast member in the film. Dana and Will also had small roles in "The Brooke Ellison Story".


title: Christopher Reeve

text: Following the first Superman movie, Reeve realized Hollywood producers wanted him to be an action star. He later said, "I found most of the scripts of the genre poorly constructed, and I felt the starring roles could easily be played by anyone with a strong physique." In addition, he did not feel he was right for the other films he was offered and turned down the lead roles in "American Gigolo", "The World According to Garp", "Splash", "Fatal Attraction", "Romancing the Stone", "Lethal Weapon", and "Body Heat". Katharine Hepburn recommended Reeve to David Lean for the role of Fletcher Christian in "The Bounty", a film version of "Mutiny on the Bounty" starring Anthony Hopkins. After considering it, Reeve decided he would be miscast, and the film was eventually made with Mel Gibson. After his 1995 accident, Reeve turned down the role of Mason Verger in "Hannibal", which was played by Gary Oldman.


title: Christopher Reeve

text: While filming the first two "Superman" movies in England, Reeve began a ten-year relationship with modeling executive Gae Exton. They had a son, Matthew Exton Reeve, on December 20, 1979, and a daughter, Alexandra Exton Reeve, in December 1983. Both were born in London, England. In February 1987, Reeve and Gae Exton separated amicably with joint custody of their children, and Reeve returned to New York. Matthew and Alexandra remained in London with their mother and often spent their holidays with Reeve.


title: Christopher Reeve

text: In June 1987, Reeve met his future wife Dana Morosini, a singer and actress. By 1991, they were living together but Reeve, remembering his parents' painful divorce and other failed marriages in his family, could not bring himself to commit. After they almost broke up, Reeve began about a year of therapy, primarily to talk through his fears about marriage. Then one night during dinner, he said "I just put down my fork and asked her to marry me." They were married in April 1992, and their son William was born on June 7, 1992. The couple remained happily married until Reeve's death.


title: Christopher Reeve

text: Reeve began his involvement in horse riding in 1985 after learning to ride for the film "Anna Karenina". He was initially allergic to horses, so he took antihistamines. He trained on Martha's Vineyard, and by 1989, he began eventing. His allergies soon disappeared. He had leg injuries as a teen while skiing, and he later broke three ribs in a riding accident he described, along with the leg injuries, on "The Tonight Show" in March 1987.


title: Christopher Reeve

text: Reeve purchased a 12-year-old American thoroughbred horse named Eastern Express, nicknamed "Buck" while filming "Village of the Damned". He trained with Buck in 1994 and planned to do Training Level events in 1995 and move up to Preliminary in 1996. Though Reeve had originally signed up to compete at an event in Vermont, his coach invited him to go to the Commonwealth Dressage and Combined Training Association finals at the Commonwealth Park equestrian center in Culpeper, Virginia. Reeve finished in fourth place out of 27 in the dressage, before walking his cross-country course. He was concerned about jumps 16 and 17 but paid little attention to the third jump, which was a routine three-foot-three fence shaped like the letter 'W'.


title: Christopher Reeve

text: On May 27, 1995, Reeve's horse made a refusal. Witnesses said the horse began the third fence jump and suddenly stopped. Reeve fell forward off the horse, holding on to the reins. His hands became tangled in them, and the bridle and bit were pulled off the horse. He landed head first on the far side of the fence, shattering his first and second vertebrae. The resulting cervical spinal injury paralyzed him from the neck down and halted his breathing. Paramedics arrived three minutes later and immediately took measures to get air into his lungs. He was taken first to the local hospital, before being flown by helicopter to the University of Virginia Medical Center. He had no recollection of the accident.


title: Christopher Reeve

text: After five days in which Reeve was heavily medicated and delirious, he regained full consciousness. His doctor explained to him his first and second cervical vertebrae had been destroyed and his spinal cord damaged. He was paralyzed from the neck down and unable to breathe without a ventilator, but had not sustained any brain damage.


title: Christopher Reeve

text: Reeve's first thoughts when informed about the seriousness of his injury was he had ruined his life, would be a burden on his family, and it might be best to "slip away". He mouthed to his wife Dana, "Maybe we should let me go." She tearfully replied, "I will support whatever you want to do, because this is your life and your decision. But I want you to know that I'll be with you for the long haul, no matter what. You're still you. And I love you." In what she would later describe as a "sales ploy", she also told him that if he still wanted to die in two years they could reconsider the question.


title: Christopher Reeve

text: After this conversation, and visits from his children in which he saw how much they needed him, Reeve consented to lifesaving surgery and to treatment for pneumonia. He never considered suicide as an option again.


title: Christopher Reeve

text: Reeve went through inner anguish in the ICU, particularly when he was alone during the night. His approaching operation to reattach his skull to his spine in June 1995 "was frightening to contemplate. ... I already knew that I had only a fifty-fifty chance of surviving the surgery. ... Then, at an especially bleak moment, the door flew open and in hurried a squat fellow with a blue scrub hat and a yellow surgical gown and glasses, speaking in a Russian accent." The man announced that he was a proctologist and was going to perform a rectal exam on Reeve. It was Robin Williams, reprising his character from the film "Nine Months". Reeve wrote: "For the first time since the accident, I laughed. My old friend had helped me know that somehow I was going to be okay." In addition to visits from friends and family, Reeve received over 400,000 letters from all over the world, which gave him great comfort during his recovery.


title: Christopher Reeve

text: Dr. John A. Jane performed surgery to repair Reeve's neck vertebrae. He put wires underneath both laminae and used bone from Reeve's hip to fit between the C1 and C2 vertebrae. He inserted a titanium pin and fused the wires with the vertebrae, then drilled holes in Reeve's skull and fitted the wires through to secure the skull to the spinal column.


title: Christopher Reeve

text: After a month in the hospital, Reeve spent five months at the Kessler Rehabilitation Center in West Orange, New Jersey to continue with his recovery and learn skills such as operating his electric sip-and-puff wheelchair by blowing air through a straw. In his autobiography "Still Me", he described initially not wanting to face the reality of his new disability. Getting used to sitting strapped into a wheelchair, or taking a shower, were initially terrifying. Reeve developed a deep fondness for many of the staff at Kessler, and through conversations with the other patients gradually started to see himself as being part of the disabled community.


title: Christopher Reeve

text: For the first few months after the accident, Reeve relied on a ventilator, which was connected to his neck through a tracheostomy tube, for every breath. With therapy and practice, he developed the ability to breathe on his own for up to 90 minutes at a time.


title: Christopher Reeve

text: Reeve exercised for up to four or five hours a day, using specialized exercise machines to stimulate his muscles and prevent muscle atrophy and osteoporosis. He believed that intense physical therapy could regenerate the nervous system, and also wanted his body to be strong enough to support itself if a cure for paralysis were found. Starting in 2000, he started to regain the ability to make small movements in his fingers and other parts of his body, and by 2002 reported that he could sense hot and cold temperatures on 65% of his body. Reeve's doctors were shocked by his improvements, which they attributed to his intensive exercise regimen.