On Discrete Gamma Distribution

Abstract

A new discrete counterpart of gamma distribution for modelling discrete life data is defined based on similar mathematical form and properties of the continuous version. The main statistical and reliability properties of this distribution are derived and it is shown that this model can deal with both over and under-dispersed data. Geometric variables and finite sum of geometric variables, i.e., negative binomial are shown to be special cases of the proposed discrete gamma. Also, the size-biased discrete gamma distribution is derived and discussed. Moreover, different estimation methods of the underlying parameters of this distribution are utilized and comparisons of their performance have been made. Finally, an application in real-life data is used to elucidate the earlier results of this article.

Keywords:

• Geometric
• Negative binomial
• Statistical properties
• Unimodality
• Reliability properties
• Reversed failure rate
• Maximum likelihood method
• Moment method

Mathematics Subject Classification:

• Primary 60E05, 60N05; Secondary 62F10, 62G05