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A new generalization of the Marshall–Olkin Gompertz distribution

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Abstract

In this paper, a new distribution of the four-parameter lifetime model called the Marshall–Olkin Gompertz is proposed on the basis of the Gompertz distribution. It is a generalization of the Marshall–Olkin Gompertz distribution having constant failure rate and can also be constant, decreasing, increasing unimodal and bathtub-shaped depending on its parameters. Some mathematical properties of this model such as the probability density function, cumulative distribution function, hazard rate function, central moments, moments of order statistics, Renyi and Shannon entropies and quantile function are derived. In addition, the maximum likelihood of its parameters method is estimated and this new distribution compared with some Gompertz distribution generalizations by means of a set of real data.

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Acknowledgements

The authors wish to thank the respected editor and reviewers for evaluation of this article.

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Authors and Affiliations

  1. Department of Statistics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran

    Shahram Yaghoobzadeh

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  1. Shahram Yaghoobzadeh
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Correspondence to Shahram Yaghoobzadeh.

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Yaghoobzadeh, S. A new generalization of the Marshall–Olkin Gompertz distribution. Int J Syst Assur Eng Manag 8 (Suppl 2), 1580–1587 (2017). https://doi.org/10.1007/s13198-017-0630-8

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  • DOI: https://doi.org/10.1007/s13198-017-0630-8

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