Re: Sum of two correlated Poisson distribution


"David Jones 写道：
"
Jacqueline wrote:
I am trying to develop the Sum of two correlated Poisson
distribution.
Given that W1, W2 and W3 are independent Poisson distribtuion with
parameter s1,s2 and s3 respectly.
Let X=W1+W3 and Y=W2+W3.

How to compute the desity funtion of Z=X+Y (distribution of the sum
of
those variables ? )

Many thanks to any kindly reply.
Jacqueline

You are possibly better off trying this a different way. You want

Z=X+Y=W1+W2+2*W3

But the probabilities for (W1+W2) are well known, since this is just
Poisson, and the probabilities for (2*W3) are easy to get, since they
are a version of the Poisson probabilities where only even values are
possible outcomes. You then have to find the probabilities for the sum
of two independent variables (W1+W2) and (2*W3).

It may be that the problem you gave is only a special case of
something more general for which the above would not work. It might be
that using probability generating functions would provide a better
approach in both the above case, and more generally.

David Jones


Thanks David,

But in literature, there have many studied to analyze the differnce of
two correlated Poisson distrution (Say, Z=X-Y). But there is little
literatural to study the sum of the two correlated Poisson distribution
(S=X+Y).

Your ways of X+Y=(W1+W2) and (2*W3) seems amaizing. I will try. But I
could hardly belive that it is so simple to handle this problem.

Thanks very much to share your knowledge with me.

Jacqueline

.

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