A New Class of Topp–Leone Power Series Distributions with Reliability Application

Rasool Roozegar, Saralees Nadarajah

    Research output: Contribution to journalArticlepeer-review


    Okasha et al. (J Failure Anal Prevention, 2017. doi:10.1007/s11668-017-0263-x) introduced the novel Topp–Leone geometric distribution. Here, we introduce a class of distributions containing [32]’s distribution as a particular case. The class of distributions contains several important distributions, including the Topp–Leone geometric, Topp–Leone Poisson, Topp–Leone logarithmic, Topp–Leone binomial and Topp–Leone negative binomial distributions. We derive comprehensive mathematical properties of the class. We obtain closed form expressions for the density function, cumulative distribution function, survival and hazard rate functions, moments, mean residual lifetime, mean past lifetime, order statistics and moments of order statistics. The class is shown to be more flexible by reanalyzing the real data set in [32].

    Original languageEnglish
    Pages (from-to)955-970
    Number of pages16
    JournalJournal of Failure Analysis and Prevention
    Issue number5
    Early online date21 Aug 2017
    Publication statusPublished - 1 Oct 2017


    • Hazard rate
    • Maximum likelihood estimation
    • Moments


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