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Marshall-Olkin generalized exponential distribution

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Abstract

Marshall and Olkin (Biometrika 641–652, 1997) introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the Marshall-Olkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory.

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Acknowledgments

The authors would like to thank two referees for their constructive comments.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences and Mathematics, University of Nis, Nis, Serbia

    Miroslav M. Ristić

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Debasis Kundu

Authors
  1. Miroslav M. Ristić
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  2. Debasis Kundu
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Correspondence to Debasis Kundu.

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Ristić, M.M., Kundu, D. Marshall-Olkin generalized exponential distribution. METRON 73, 317–333 (2015). https://doi.org/10.1007/s40300-014-0056-x

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  • DOI: https://doi.org/10.1007/s40300-014-0056-x

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