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)