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A generalization of discrete Weibull distribution

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  • K. Jayakumar
  • K. K. Sankaran

Abstract

In this paper, we introduce a new family of discrete distributions and study its properties. It is shown that the new family is a generalization of discrete Marshall-Olkin family of distributions. In particular, we study generalized discrete Weibull distribution in detail. Discrete Marshall-Olkin Weibull distribution, exponentiated discrete Weibull distribution, discrete Weibull distribution, discrete Marshall-Olkin generalized exponential distribution, exponentiated geometric distribution, generalized discrete exponential distribution, discrete Marshall-Olkin Rayleigh distribution and exponentiated discrete Rayleigh distribution are sub-models of generalized discrete Weibull distribution. We derive some basic distributional properties such as probability generating function, moments, hazard rate and quantiles of the generalized discrete Weibull distribution. We can see that the hazard rate function can be decreasing, increasing, bathtub and upside-down bathtub shape. Estimation of the parameters are done using maximum likelihood method. A real data set is analyzed to illustrate the suitability of the proposed model.

Suggested Citation

  • K. Jayakumar & K. K. Sankaran, 2018. "A generalization of discrete Weibull distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(24), pages 6064-6078, December.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:24:p:6064-6078
    DOI: 10.1080/03610926.2017.1406115
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    Cited by:

    1. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.

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