MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This should be a very easy answer for those who know the distribution. Lately, I am dealing a lot with the following distribution:


It is obtained by raising a gamma distributed random variable with shape $u$ and scale $s$ to the power $\frac{1}{p}$ ($p>0$). The resulting distribution is a generalization of the $\chi$-distribution (for $p=2$ and $u=\frac{n}{p}$) or, for arbitrary $p>0$, the generalization of the radial distribution of a multivariate $p$-generalized Normal (for $u=\frac{n}{p}$).

My question is: Is there an "official" name for that distribution?

share|cite|improve this question

Unless I am mistaken, this distribution could be called a $p$-Gamma distribution because the Gamma distribution is Infinitely Divisible

share|cite|improve this answer
I cannot follow your reasoning. Could you explain please? – fabee Aug 19 '11 at 20:13
My only point was that since it does not have an official name, calling it a Gamma or a $p$-Gamma distribution is a reasonable choice of name. – Suvrit Aug 21 '11 at 21:34
up vote 1 down vote accepted

I found the answer. It is embarrassingly simple: The distribution is called Generalized Gamma Distribution. Who would have thought of that? The corresponding publication is:

Stacy EW. A Generalization of the Gamma Distribution. The Annals of Mathematical Statistics. 1962;33(3):pp. 1187-1192. Available at:

share|cite|improve this answer

I don't know of a name for a general power of a general gamma distribution. But here are two special cases.

If the power is -1 and the gamma shape arbitrary, it's an inverse gamma distribution. And if the power is arbitrary and the gamma shape is 1 (i.e. exponential) then it's a Weibull distribution.

share|cite|improve this answer
That's what got me thinking whether there's name for it: It contains so many special cases. – fabee Aug 19 '11 at 14:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.