# Minimum of i.i.d ~gamma random variables

1. Feb 8, 2008

### Pere Callahan

Hi,

Another question...

I know that the minimum of n i.i.d $$\lambda$$-exponentially distributed random variables is again exponentially distributed (with parameter $$n\lambda$$). Is something similar true for $$\Gamma(k,\theta)$$ ....? that is, is the minimum of n i.i.d Gamma distributed random variables again Gamma distributed... or is it some other well known distribution?

I also know about the extreme-value theorem which might be of use if I were only interested in large n (which is actually the case) but an explicit distribution seems always better to me.