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The modified Weibull geometric distribution

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Abstract

A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes.

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Acknowledgments

The authors wish to thank the editor and two referees for their valuable suggestions that led to an improvement of the paper. The first author was partially supported by the New Faculty Start-Up Fund at Michigan Technological University.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Min Wang

  2. Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Cairo, 12613, Egypt

    Ibrahim Elbatal

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  1. Min Wang
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  2. Ibrahim Elbatal
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Correspondence to Min Wang.

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Wang, M., Elbatal, I. The modified Weibull geometric distribution. METRON 73, 303–315 (2015). https://doi.org/10.1007/s40300-014-0052-1

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  • DOI: https://doi.org/10.1007/s40300-014-0052-1

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