A Generalized Poisson Distribution

Abstract

Cumulative probabilities of a Poisson distribution can be written in terms of incomplete gamma function where the parameter of the gamma function is an integer. From this definition a new generalization of the Poisson distribution is obtained with two parameters. Asymptotic behavior of this distribution is shown to be normal. Some order properties of this distribution are also studied.

Keywords:

• Discrete hazard rate
• Goodness of fit
• Incomplete gamma function
• Likelihood ratio order
• Moment generating function
• Poisson distribution
• Stochastic order

Mathematics Subject Classification:

• Primary 62E15
• Secondary 60E15

Acknowledgment

The authors are thankful to the reviewers and the Associate Editor for several constructive suggestions that helped to effectively improve the article.