Journal of Mathematics and Statistics

A General Probability Distribution Using Burmann Power Series

Pali Sen and Richard F. Patterson

DOI : 10.3844/jmssp.2005.189.193

Journal of Mathematics and Statistics

Volume 1, Issue 3

Pages 189-193


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.


© 2005 Pali Sen and Richard F. Patterson. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.