How variable are percentiles?










import scipy as sp
import scipy.stats
import scipy.special
import matplotlib.pyplot as plt

def pdf(y, n, k):
    Phi = scipy.stats.norm.cdf(y)
    phi = scipy.stats.norm.pdf(y)

def plot_percentile(p):
    center = scipy.stats.norm.ppf(0.01*p)



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5 thoughts on “How variable are percentiles?

  1. I’ll comment. If we simulate a mathematical blob like the 3x+1 function, then statistical models are really just non-rigorous guessing games that we honestly cannot “expect” to mean anything at all.

    When simulating something real world, it seems like an error budget is a key part of any model. For example, a great error buget shows us that the pioneer spaceceaft saw what we can call an anomalous acceleration towards the sun. A closer look a TWT operation tells us that no matter how well the tube design, there exists a parasitic effect, see Pierce, causing f_out to always be greater than f_in. This effect looks big enough to explain the anomaly, i.e., would look like a blue shift, would show up in the signal similar to the doppler effect, and further there was a change in the magnatude of the effect when one craft switched to the back-up tube.

  2. Apologies if I am mistaken here, but …

    The 50th, 75th, 90th, and 95th percentiles of the standard normal are approximately 0; 0.6745; 1.2816; and 1.6449, respectively.

    To my eye, it looks to me that your plots are NOT actually centered on those values, and the distributions ARE centered on those values (and perhaps not biased after all).

    I am not a Python expert, but it looks like you were trying to plot an interval of width 0.25 units on each side of the center, for a total width of 0.5; but your plots are all 0.6 units wide, so maybe Python did something behind your back?

    Sorry if I am totally off-base here.

  3. I have difficulty understanding the paper, what is the captial Phi function in equation (2)?

  4. Andrew: Phi is the cumulative density function of a standard normal random variable. And phi (lower case) is its derivative, the corresponding probability density function.

    You can read more detail here.

  5. John, those plots are a bit confusing. The x scale is the same but the values vary and the centring of the plots is not quite the same. More importantly, though, the y scales vary too, so I can’t really compare their heights. If the heights aren’t really there to be compared, normalize them to the same height.

    Ideally though, wouldn’t these be on one plot? Normalized, centred, etc. Then I can see the how much wider they get.

    Perhaps all that’s needed is a simple plot of the FWHM value for all these distributions versus the percentage?

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