A Size Biased Polya-Aeppli Distribution and Its Applications

Abstract

This paper is concerned with a new extension to Polya-Aeppli distribution called as size-biased Polya-Aeppli distribution (SBPAD). This SBPAD consists of two parameters and these are estimated by method of proportion of one’th cell (MPOC), method of moments (MM) including the estimating equations and maximum likelihood estimation (MLE). The expressions of its moment and probability generating functions have also been derived giving the relationship between mean and variance of SBPAD. At the end, the applications of the distribution to various four sets of data have also been added and found that the distribution describes the pattern of the data satisfactorily well.