Talk:Beta prime distribution

Beta Prime and F

The comment about Beta Prime and F appears to be incorrect. Although it makes sense that these are related the statement that if b is beta prime, then b*alpha/beta is F can't make sense, since if alpha = beta then you just get b and F distribution is not invariant when you multiply d1 and d2 by constants. —Preceding unsigned comment added by 83.244.153.18 (talk) 11:31, 7 April 2010 (UTC)

Cumulative distribution function and excess kurtosis

Dear main authors: as you probably know, the beta-prime distribution is the same as the F-distribution, if one replaces in the latter: $d_{1}/2\rightarrow \alpha$, $d_{2}/2\rightarrow \beta$, $d_{1}x/d_{2}\rightarrow x$. That means that part of the text in the F-distribution-article can be copied and pasted into this article. That's what I did for the CDF and the kurtosis. Regards: Herbmuell (talk) 17:59, 21 July 2015 (UTC).

Also on the relation between Beta Prime and F

${\tfrac {\alpha }{\beta }}$ should be flipped to get

If $X\sim F(2\alpha ,2\beta )$ has an F-distribution, then ${\tfrac {\alpha }{\beta }}X\sim \beta '(\alpha ,\beta )$, or equivalently, $X\sim \beta '(\alpha ,\beta ,1,{\tfrac {\beta }{\alpha }})$.

Alternative parameterization does not match parameters from sidebox

The sidebox of the article states that the mean and variance of the distributions are

$\mu ={\frac {\alpha }{\beta -1}}{\text{ if }}\beta >1$

and

$v={\frac {\alpha (\alpha +\beta -1)}{(\beta -2)(\beta -1)^{2}}}{\text{ if }}\beta >2$

However, solving the system of equations for $\alpha$ and $\beta$ shows the alternate parameterization should be

$\alpha =\mu (\beta -1)$

and

$\beta ={\frac {\mu (\mu +1)}{v}}+2$

So the given $\beta$ solution in the text is incorrect — Preceding unsigned comment added by 198.208.46.92 (talk) 23:57, 20 June 2022 (UTC)