A General Probability Distribution Using Burmann Power Series

Abstract

The goal of this study is to present a general power series distribution that exhibits the properties of some well known distributions. To accomplish this goal we examine an infinite sequence of independent random variables having a Bürmann’s power series distribution. Consequently, we derive moment generating function of the distribution and establish the maximum likelihood estimate of the component that can be attributed to the parameter of the distribution. Using the results mentioned above we verify our conjecture on two known parametric discrete distributions, the Poisson and the Binomial.