Beta prime distribution

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A Beta Prime Distribution is a probability distribution defined for x>0 with two parameters (of positive real part), α and β, having the probability density function:

where B is a Beta function. 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 mode of a variate X distributed as β^'(α,β) is . Its mean is and its variance is .

If X is a β^'(α,β) variate then is a β^'(β,α) variate.

If X is a β(α,β) then and are β^'(β,α) and β^'(α,β) variates.

If X and Y are γ(α₁) and γ(α₂) variates, then is a β^'(α₁,α₂) variate.

[edit] Reference

MathWorld article

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