On bayes allocation of the sample for estimation of the mean when each stratum has a poisson distribution

Abstract

Consider a stratified population with L strata, so that a Poisson random variable is associated with each stratum. The parameter associated with the hth stratum is L. Let πh be the known proportion of the population in the hth stratum. We want to estimate the parameter We assume that prior information is available on θh and that it can be expressed in terms of a gamma distribution with parameters αh and βh . We also assume that the prior distributions are independent Using squared error loss function, a Bayes allocation of total sample size with a cost constraint is given. The Bayes estimate using the Bayes allocation is shown t o have an adjusted mean square error which is strictly less than the adjusted mean square error of the classical estimate using the classical allocation.