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Minimum of i.i.d ~gamma random variables

  1. Feb 8, 2008 #1
    Hi,

    Another question...

    I know that the minimum of n i.i.d [tex]\lambda[/tex]-exponentially distributed random variables is again exponentially distributed (with parameter [tex]n\lambda[/tex]). Is something similar true for [tex]\Gamma(k,\theta)[/tex] ....? 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.

    Thanks for any answers

    -Pere
     
  2. jcsd
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