Family of generalized gamma distributions

Properties and applications

Ayman Alzaatreh, Carl Lee, Felix Famoye

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    In this paper, a family of generalized gamma distributions, T -gamma family, has been proposed using the T -R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic and extreme value distributions. Several general properties of the T -gamma family are studied in details including moments, mean deviations, mode and Shannon’s entropy. Three new generalizations of the gamma distribution which are members of the T -gamma family are developed and studied. The distributions in the T -gamma family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Four data sets with various shapes are fitted by using members of the T -gamma family of distributions.

    Original languageEnglish
    Pages (from-to)869-886
    Number of pages18
    JournalHacettepe Journal of Mathematics and Statistics
    Volume45
    Issue number3
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    Generalized gamma Distribution
    Logistics
    Extreme Value Distribution
    Quantile Function
    Mean deviation
    Bimodal
    Gamma distribution
    Family
    Entropy
    Moment

    Keywords

    • Bimodality
    • Quantile function
    • Shannon’s entropy
    • T -R{Y} framework

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Analysis
    • Geometry and Topology
    • Statistics and Probability

    Cite this

    Family of generalized gamma distributions : Properties and applications. / Alzaatreh, Ayman; Lee, Carl; Famoye, Felix.

    In: Hacettepe Journal of Mathematics and Statistics, Vol. 45, No. 3, 2016, p. 869-886.

    Research output: Contribution to journalArticle

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