Journal of Failure Analysis and Prevention

, Volume 17, Issue 5, pp 955–970 | Cite as

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

  • Rasool Roozegar
  • Saralees Nadarajah
Technical Article---Peer-Reviewed


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].


Hazard rate Maximum likelihood estimation Moments 


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Copyright information

© ASM International 2017

Authors and Affiliations

  1. 1.Department of StatisticsYazd UniversityYazdIran
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK

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