`scipy.stats._continuous_distns:irwinhall_gen`

source: /scipy/stats/_continuous_distns.py :9359

Signature

   class     irwinhall_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

An Irwin-Hall (Uniform Sum) continuous random variable.

Extended Summary

An Irwin-Hall continuous random variable is the sum of $n$ independent standard uniform random variables ^[1] ^[2].

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Notes

Applications include Rao's Spacing Test, a more powerful alternative to the Rayleigh test when the data are not unimodal, and radar ^[3].

Conveniently, the pdf and cdf are the $n$ -fold convolution of the ones for the standard uniform distribution, which is also the definition of the cardinal B-splines of degree $n - 1$ having knots evenly spaced from $1$ to $n$ ^[4] ^[5].

The Bates distribution, which represents the mean of statistically independent, uniformly distributed random variables, is simply the Irwin-Hall distribution scaled by $1/ n$ . For example, the frozen distribution bates = irwinhall(10, scale=1/10) represents the distribution of the mean of 10 uniformly distributed random variables.

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Aliases

scipy.stats._continuous_distns.irwinhall_gen