Talk:Compound Poisson distribution

From Wikipedia, the free encyclopedia

Mathematics Portal

This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.

Mathematics rating:

Stub Class

Low Priority

Field: Probability and statistics

Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments.
Please add to or update the comments to suggest improvements to the article.
Introduction and structure would help - nearly start class. Geometry guy 18:37, 21 May 2007 (UTC)

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.

[edit] Some properties

$E [Y] = E [E [Y | N]] = λ E [X]$

$V a r [Y] = V a r [E [Y | N]] + E [V a r [Y | N]] = λ{E 2 [X] + V a r [X]}$

The cumulant generating function $K_Y(t)=\mbox{ln} E[e^{tY}]=\mbox{ln} E[E[e^{tY}|N]]=\mbox{ln} E[e^{NK_X(t)}]=K_N(K_X(t))$

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)

Talk:Compound Poisson distribution

From Wikipedia, the free encyclopedia

[edit] Some properties

Views

Navigation

Interaction

Search