scipy.stats._continuous_distns:betaprime_gen

Notes

The probability density function for betaprime is:

for $x>=0$, $a>0$, $b>0$, where $\beta (a,b)$ is the beta function (see scipy.special.beta).

betaprime takes a and b as shape parameters.

The distribution is related to the beta distribution as follows: If $X$ follows a beta distribution with parameters $a,b$, then $Y=X/(1-X)$ has a beta prime distribution with parameters $a,b$ (^[1]).

The beta prime distribution is a reparametrized version of the F distribution. The beta prime distribution with shape parameters a and b and scale = s is equivalent to the F distribution with parameters d1 = 2*a, d2 = 2*b and scale = (a/b)*s. For example,

>>> from scipy.stats import betaprime, f
>>> x = [1, 2, 5, 10]
>>> a = 12
>>> b = 5
>>> betaprime.pdf(x, a, b, scale=2)
array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
>>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)
array([0.00541179, 0.08331299, 0.14669185, 0.03150079])

%(after_notes)s