Talk:Compound Poisson distribution
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
|WikiProject Statistics||(Rated Start-class, Low-importance)|
I assume that E[Y] = λ * E[X]
What is Var[Y] in terms of the distribution of X? Say, if X has a gamma distribution.
The cumulant generating function
- One could add to the above, that if N has a Poisson distribution with expected value 1, then the moments of X are the cumulants of Y. Michael Hardy 20:39, 23 Apr 2005 (UTC)
Why is ?
I would have thought that the process should be started in zero? Just thinking in terms of (shudder) actuarial science, a claims process would make very little sense if it started with a claim at time zero? What I'm proposing is to change the definition to the one given on the page for 'Compound Poisson Process'. — Preceding unsigned comment added by Fladnaese (talk • contribs) 18:54, 26 May 2011 (UTC)
I see that a citation is needed for the relationship between the cumulants of the compound Poisson distribution Y, and the moments for the random variables Xi. Back in 1976, I proved this result, that is:
For j > 0, K(j) = lambda * m(j), where:
- K(j) are the cumulants of Y - m(j) are the moments for the Xi - lambda is the parameter of the Poisson distribution
I made use of the characteristic function in thís proof. Is my proof of interest as a citation? If so, I can send the reference number and a pdf of the paper I wrote.