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Encyclopedia > Beta prime distribution

A Beta Prime Distribution is a distribution with probability function:


P(x) = frac{x^(alpha-1) (1+x)^{-alpha -beta}}{B(alpha,beta)}


where B is a Beta function.


The mode of a variate X distributed as β'(α,β) is hat{X} = frac{alpha-1}{beta+1}.


If X is a β'(α,β) variate then frac{1}{X} is a β'(β,α) variate.


If X is a β'(α,β) then frac{1-X}{X} and frac{X}{1-X} are β'(β,α) and β'(α,β) variates.


If X and Y are γ(α1) and γ(α2) variates, then frac{X}{Y} is a β'12) variate.


If frac{X^2}{2} and frac{Y^2}{2} are gamma(frac{1}{2}) variates, then Z^2 = left(frac{X}{Y}right)^2 is a beta^{'}(frac{1}{2},frac{1}{2}) variate.


M.E. - November 2005


  Results from FactBites:
 
probability distribution: Definition and Much More from Answers.com (1593 words)
The Beta distribution on [0,1], of which the uniform distribution is a special case, and which is useful in estimating success probabilities.
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Beta distribution - Wikipedia, the free encyclopedia (597 words)
The Dirichlet distribution is the multivariate generalization of the beta distribution.
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