A New Reciprocal Weibull Extension for Modeling Extreme Values with Risk Analysis under Insurance Data

Haitham M. Yousof, Yusra Tashkandy, Walid Emam, M. Masoom Ali and Mohamed Ibrahim ()
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Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt
Yusra Tashkandy: Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Walid Emam: Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
M. Masoom Ali: Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA
Mohamed Ibrahim: Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta 34517, Egypt

Mathematics, 2023, vol. 11, issue 4, 1-26

Abstract: Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as essential critical risk indicators. Five key risk indicators, including value-at-risk, tail variance, tail-value-at-risk, and tail mean-variance, were also used for describing the risk exposure under the reinsurance revenues data. These measurements were created for the proposed model; hence, this paper presents a novel distribution for this purpose. Relevant statistical properties are derived, including the generating function, ordinary moments, and incomplete moments. Special attention is devoted to the applicability of the new model under extreme data sets. Three applications to real data show the usefulness and adaptability of the proposed model. The new model proved its superiority against many well-known related models. Five key risk indicators are employed for analyzing the risk level under the reinsurance revenues dataset. An application is provided along with its relevant numerical analysis and panels. Some useful results are identified and highlighted.

Keywords: extreme values; insurance data; reciprocal Weibull model; geometric family; simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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