Compound poisson distributions: Properties and estimation*

Abstract

Multivariate compound Poisson distribution is obtained by m p-independent Poisson distributions with a mixing distribution. marginal, conditional probability mass function and moments of comp Poisson distribution when the mixing parameter has a gamma distribu are obtained. The parameters of the mixed distribution are then estirr under a normalized squared error loss. The improved estimators obtained over the unbiased estimators for ' p> = 2, by solving ce difference inequality. Also robustness of the Clevenson-Zidek type estin is shown when the p-distributions are dependent through the m process. Risk simulations studies are obtained to show the amoui improvements.

Keywords:

• Compound Poisson distribution
• Proba generating Junction
• Unbiasedness
• Simultaneous estimation
• Normc squared error loss
• Clevenson-Zidek's estimator