Some Properties, Characterization and an Application of Mittag-Leffler type Poisson distribution

Abstract

Probability distributions analyze the complex phenomena in a comprehensive way and provide the possible solutions of the understudy problem. The characteristics of a probability distribution describe its behavior and check its compatibility for modeling the data. The present research involves an extensive study of Mittag-Leffler type Poisson (MLTP) distribution developed by Porwal and Dixit (2017). They used Mittag-Leffler function, a mathematical function/series, to develop a new probability distribution. This function has been extensively used in the fields of mathematics, engineering, medical and social sciences. Some mathematical properties of the MLTP distribution are discussed. Graphical representation of MLTP distribution is provided for different values of the parameters. The moment generating function, characteristic function and order statistic are also studied. Characterizations for the sum of the random variables are presented. The distributions of product and ratio of two MLTP random variables are derived. In addition, the estimates of unknown parameters of MLTP distribution are obtained by using the method of maximum likelihood estimation. The MLTP distribution is applied to three real life data sets from the medical field. The log-likelihood values, AIC and BIC of the present model are compared with those of some other distributions extant in the literature.