The Extended Log-Logistic Distribution: Inference and Actuarial Applications

Nada M. Alfaer, Ahmed M. Gemeay, Hassan M. Aljohani and Ahmed Z. Afify
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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

Mathematics, 2021, vol. 9, issue 12, 1-22

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.

Keywords: insurance losses data; expected shortfall; log-logistic distribution; parameter estimation; risk measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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