The Poisson-conjugate Lindley mixture distribution

ABSTRACT

A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model.

Keywords:

• Geometric distribution
• Mixture
• Natural exponential family
• EM algorithm

Mathematics Subject Classification:

• 62P25; 62P99

Acknowledgments

EGD thanks MICINN (Spain) (project ECO2009-14152) for partial support of this work. The authors are indebted to the Associate Editor and the anonymous referees for helpful comments which, without (a) doubt, helped to improve an earlier version of this article.