R-distribution Distribution#

A general-purpose distribution with a variety of shapes controlled by one shape parameter c>0. The support of the standard distribution is x[1,1].

f(x;c)=(1x2)c/21B(12,c2)F(x;c)=12+xB(12,c2)2F1(12,1c2;32;x2)
μn=(1+(1)n)2B(n+12,c2)

The R-distribution with parameter n is the distribution of the correlation coefficient of a random sample of size n drawn from a bivariate normal distribution with ρ=0. The mean of the standard distribution is always zero and as the sample size grows, the distribution’s mass concentrates more closely about this mean.

Implementation: scipy.stats.rdist