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General results on bivariate extended Weibull Morgenstern family and concomitants of its generalized order statistics

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Abstract

In this paper, we develop the extended Weibull family of distributions to a bivariate class using the Farlie–Gumbel–Morgenstern copula. This is called the bivariate Farlie–Gumbel–Morgenstern extended Weibull family, and some of its properties are investigated. Some special cases of this family and their correlation coefficient are found. Also, the maximum correlation coefficient of most special cases is investigated. We study the concomitants of generalized order statistics from this new class of Morgenstern bivariate distribution and obtain some relevant relations for single and product moments of concomitants. Some well-known information measures such as the Shannon entropy and extropy for concomitants are derived.

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Acknowledgements

The authors are grateful to the anonymous referee for the helpful comments and suggestions to improve this manuscript.

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Authors and Affiliations

  1. Department of Statistics, Yazd University, Yazd, Iran

    A. A. Jafari & Z. Almaspoor

  2. Department of Statistics, Persian Gulf University, Bushehr, Iran

    S. Tahmasebi

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  1. A. A. Jafari
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  2. Z. Almaspoor
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  3. S. Tahmasebi
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Jafari, A.A., Almaspoor, Z. & Tahmasebi, S. General results on bivariate extended Weibull Morgenstern family and concomitants of its generalized order statistics. Ricerche mat (2021). https://doi.org/10.1007/s11587-021-00680-3

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