Re: Sum of gamma distributed random variables


http://mathworld.wolfram.com/GammaDistribution.html
has one answer at least one (2)

(1) from wiki it should be gamma(p+q,v)

correspondingly (2) is correct.

(3) might not be correct..I am thinking of replacing x in the pdf with
x/c (am referring to the scalar you refer to as c) and seeing if I can group
it with either p or v .. doest seem likely. I might be wrong.



On Tue, 11 Mar 2008 15:40:39 -0400, Michael Haenlein <haenlein@xxxxxxxxx> wrote:

Dear all,

I have three questions regarding summing up gamma distributed random
variables:

(1) Is there a closed-form expression for the sum of two gamma random
variables that have the same scale parameter but different shape
parameters? Essentially, what's the sum of a gamma (p,v) random
variable and a gamma (q,v) random variable (p being the shape
parameter and v the scale parameter)?

(2) I think to remember that the sum of n i.i.d. gamma (p, ν) random
variables is itself distributed gamma with shape parameter pn and
scale parameter ν. Is this correct?

(3) Another think I have in mind is that a gamma (p, ν) random
variable multiplied by the scalar 1/x is itself distributed gamma with
shape parameter p and scale parameter νx. Again, is this correct?

Thanks very much for your help in advance,

Michael

.

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