Journal of Failure Analysis and Prevention

, Volume 17, Issue 3, pp 477–489 | Cite as

A New Family of Topp and Leone Geometric Distribution with Reliability Applications

  • Hassan M. Okasha
Technical Article---Peer-Reviewed


In this paper, a new class of lifetime distribution, which is called Topp–Leone (J-shaped) geometric distribution, is obtained by compound of the Topp–Leone and geometric distributions. Reliability and statistical properties of the new distribution such as quantiles, moment, hazard rate, reversed hazard rate, mean residual life, mean inactivity time, entropies, moment generating function, order statistics and their stochastic orderings are obtained. Estimation of the model parameters by least squares, weighted least squares, maximum likelihood and the observed information matrix are derived. Finally, a real data set is analyzed for illustrative purposes.


Topp–Leone distribution Geometric distribution Bathtub failure rate Mean residual life Mean inactivity time Stochastic ordering Order statistics Maximum likelihood estimation Reliability applications Simulation 


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Copyright information

© ASM International 2017

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of ScienceKing Abdul Aziz UniversityJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceAl-Azhar UniversityNasr City, CairoEgypt

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