Re: Sum of two correlated Poisson distribution

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


.

Relevant Pages

  • Re: Sum of two correlated Poisson distribution
    ... How to compute the desity funtion of Z=X+Y (distribution of the sum ... Poisson, and the probabilities for are easy to get, since they ... You then have to find the probabilities for the sum ... literatural to study the sum of the two correlated Poisson distribution ...
    (sci.stat.math)
  • Re: Confirmation of Shannons Mistake about Perfect Secrecy of One-time-pad
    ... you cannot use the distribution on K to determine ... c not fixed so the distribution of K is uniform ... Computing the conditional probabilities. ... (sum of probabilities of all events where M=0 and C=0)/ ...
    (sci.math)
  • Re: Sum of two correlated Poisson distribution
    ... How to compute the desity funtion of Z=X+Y (distribution of the sum ... Poisson, and the probabilities for are easy to get, since they ... You then have to find the probabilities for the sum ...
    (sci.stat.math)
  • No result is likely - Part IV (conclusion)
    ... "When do the dice know that it's time to give the player the win so ... To sum up: ... to be able to calculate the probabilities of different outcomes, ...
    (rec.gambling.craps)
  • Re: A modest proposal (was Calculus XOR Probability)
    ... Tony Orlow wrote: ... over an infinite set of possibilities is not well handled by the ... classical notion that all individual probabilities sum to 1, ... the individual probabilities are considered equal to zero. ...
    (sci.math)