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

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Abstract

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].

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Authors and Affiliations

  1. Department of Statistics, Yazd University, P.O. Box 89195-741, Yazd, Iran

    Rasool Roozegar

  2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

Authors
  1. Rasool Roozegar
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  2. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Roozegar, R., Nadarajah, S. A New Class of Topp–Leone Power Series Distributions with Reliability Application. J Fail. Anal. and Preven. 17, 955–970 (2017). https://doi.org/10.1007/s11668-017-0329-9

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  • DOI: https://doi.org/10.1007/s11668-017-0329-9

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