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A new family of distributions based on probability generating functions

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Abstract

This paper examines a method for generating new classes of distributions which arise naturally in practice. The generated classes of distributions include the well known Marshall and Olkin class of distributions and can be thought of as mixing two discrete distributions or a discrete distribution with an absolutely continuous distribution. Properties of these classes of distributions are derived and a number of existing results in the literature are recovered as special cases. Finally, failure rates for a special class of distributions which are obtained when the discrete distribution is assumed to have a Harris form are given.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Faculty of Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    Emad-Eldin A. A. Aly & Lakdere Benkherouf

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  1. Emad-Eldin A. A. Aly
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  2. Lakdere Benkherouf
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Correspondence to Emad-Eldin A. A. Aly.

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Aly, EE.A.A., Benkherouf, L. A new family of distributions based on probability generating functions. Sankhya B 73, 70–80 (2011). https://doi.org/10.1007/s13571-011-0017-9

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  • DOI: https://doi.org/10.1007/s13571-011-0017-9

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