The Poisson-X family of distributions

M. H. Tahir, M. Zubair, Gauss M. Cordeiro, Ayman Alzaatreh, M. Mansoor

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Recently, Ristić and Nadarajah [A new lifetime distribution. J Stat Comput Simul. 2014;84:135–150] introduced the Poisson generated family of distributions and investigated the properties of a special case named the exponentiated-exponential Poisson distribution. In this paper, we study general mathematical properties of the Poisson-X family in the context of the T-X family of distributions pioneered by Alzaatreh et al. [A new method for generating families of continuous distributions. Metron. 2013;71:63–79], which include quantile, shapes of the density and hazard rate functions, asymptotics and Shannon entropy. We obtain a useful linear representation of the family density and explicit expressions for the ordinary and incomplete moments, mean deviations and generating function. One special lifetime model called the Poisson power-Cauchy is defined and some of its properties are investigated. This model can have flexible hazard rate shapes such as increasing, decreasing, bathtub and upside-down bathtub. The method of maximum likelihood is used to estimate the model parameters. We illustrate the flexibility of the new distribution by means of three applications to real life data sets.

Original languageEnglish
Pages (from-to)2901-2921
Number of pages21
JournalJournal of Statistical Computation and Simulation
Issue number14
Publication statusPublished - Sep 21 2016


  • Cauchy distribution
  • Poisson distribution
  • Poisson power Cauchy distribution
  • Poisson-X family
  • T-X family
  • generalized Poisson distribution
  • power Cauchy distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The Poisson-X family of distributions'. Together they form a unique fingerprint.

Cite this