The Poisson-X family of distributions

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

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    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)1-21
    Number of pages21
    JournalJournal of Statistical Computation and Simulation
    DOIs
    Publication statusAccepted/In press - Jan 26 2016

    Fingerprint

    Siméon Denis Poisson
    Hazards
    Poisson distribution
    Maximum likelihood
    Hazard Rate Function
    Entropy
    Mean deviation
    Linear Representation
    Lifetime Distribution
    Hazard Rate
    Shannon Entropy
    Continuous Distributions
    Quantile
    Exponential distribution
    Cauchy
    Maximum Likelihood
    Generating Function
    Lifetime
    Flexibility
    Family

    Keywords

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

    ASJC Scopus subject areas

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

    Cite this

    The Poisson-X family of distributions. / Tahir, M. H.; Zubair, M.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.

    In: Journal of Statistical Computation and Simulation, 26.01.2016, p. 1-21.

    Research output: Contribution to journalArticle

    Tahir, M. H. ; Zubair, M. ; Cordeiro, Gauss M. ; Alzaatreh, Ayman ; Mansoor, M. / The Poisson-X family of distributions. In: Journal of Statistical Computation and Simulation. 2016 ; pp. 1-21.
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    AU - Zubair, M.

    AU - Cordeiro, Gauss M.

    AU - Alzaatreh, Ayman

    AU - Mansoor, M.

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    KW - generalized Poisson distribution

    KW - Poisson distribution

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    KW - power Cauchy distribution

    KW - T-X family

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