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An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data

Author

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  • Ahmed M. T. Abd El-Bar

    (Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
    Department of Mathematics, College of Science, Taibah University, Al-Madina 41411, Saudi Arabia)

  • Willams B. F. da Silva

    (Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil)

  • Abraão D. C. Nascimento

    (Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil)

Abstract

In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.

Suggested Citation

  • Ahmed M. T. Abd El-Bar & Willams B. F. da Silva & Abraão D. C. Nascimento, 2021. "An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data," Mathematics, MDPI, vol. 9(23), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3108-:d:693686
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    References listed on IDEAS

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