- Beta prime distribution
name =Beta Prime| type =density
parameters = shape (real)
cdf =where is the Gauss's hypergeometric function 2F1
A Beta Prime Distribution is a
probability distributiondefined for x>0 with two parameters (of positive real part), α and β, having the probability density function:
where is a
Beta function. This distribution is also known [Johnson et al (1995), p248] as the beta distribution of the second kind. It is basically the same as the F distribution--if b is distributed as the beta prime distribution Beta'(α,β), then bβ/α obeys the F distribution with 2α and 2β degrees of freedom. The distribution is a Pearson type VI distribution [Johnson et al (1995), p248] .
The mode of a variate distributed as is .Its mean is if (if the mean is infinite, in other words it has no well defined mean)and its variance is if .
If X is a variate then is a variate.
If X is a then and are and variates.
If X and Y are and variates, then is a variate.
Jonhnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariuate Distributions, Volume 2 (2nd Edition), Wiley. ISBN 0-471-58494-0
[http://mathworld.wolfram.com/BetaPrimeDistribution.html MathWorld article]
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