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.
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