• Product of two independent Poisson distributions

    From jeera101@gmail.com@21:1/5 to Jacob JKW on Tue Apr 30 09:59:48 2019
    On Monday, June 14, 2010 at 2:00:45 AM UTC+5, Jacob JKW wrote:
    On Jun 13, 9:24 am, Jacob JKW <jacob...@yahoo.com> wrote:
    On Jun 10, 5:18 am, Jacob JKW <jacob...@yahoo.com> wrote:> On Jun 10, 4:47 am, Torsten Hennig <Torsten.Hen...@umsicht.fhg.de>
    wrote:> > How would one characterize the distribution of the
    product of 2
    independent Poisson distributions?

    I know the pmf simplifies to:


    So apparently this "distribution" behaves asymptotically (as L1*L2 ==> infinity) as follows:
    mean ==> L1*L2
    variance ==> mean/2
    skew ==> StdDev/sqrt(mean)
    kurtosis ==> 0.5/sqrt(mean)

    Does this match with any well-known distributions?
    Sorry, I had mistyped. Mean should have been the square root of the

    But the following appears more accurate anyway.

    Let L = L1*L2 (the product of the two Poisson parameters)

    mean ==> ~ sqrt(L - sqrt(L)/2) =~ sqrt(L) - 1/4
    E(X^2) == L (exact)
    skew ==> ~ sqrt(0.5/sqrt(L))
    kurt ==> ~ skew^2

    Does any of this mean anything to anyone? I only make such a big deal
    out of it because it does appear to describe my data with decent

    After 9 years of your question, I am facing the same problem. :)
    Did you find a solution to it?

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