• #### 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:

(L1*L2)^n/(n!)^2/I_Sub0(2*SQRT(L1*L2))

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
product.

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
accuracy.

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

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