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The Extended Log-Logistic Distribution: Inference and Actuarial Applications

Author

Listed:
  • Nada M. Alfaer

    (Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Ahmed M. Gemeay

    (Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt)

  • Hassan M. Aljohani

    (Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Ahmed Z. Afify

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

Abstract

Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called the extended log-logistic (Ex-LL) distribution, to model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, an increasing shape, a J shape, a decreasing shape, and a reversed-J shape. We derived five important risk measures based on the Ex-LL distribution. The Ex-LL parameters were estimated using different estimation methods, and their performances were assessed using simulation results. Finally, the performance of the Ex-LL distribution was explored using two types of real data from the engineering and insurance sciences. The analyzed data illustrated that the Ex-LL distribution provided an adequate fit compared to other competing distributions such as the log-logistic, alpha-power log-logistic, transmuted log-logistic, generalized log-logistic, Marshall–Olkin log-logistic, inverse log-logistic, and Weibull generalized log-logistic distributions.

Suggested Citation

  • Nada M. Alfaer & Ahmed M. Gemeay & Hassan M. Aljohani & Ahmed Z. Afify, 2021. "The Extended Log-Logistic Distribution: Inference and Actuarial Applications," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1386-:d:575194
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    References listed on IDEAS

    as
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