Classical and Bayesian inference of the weighted-exponential distribution with an application to insurance data

Fathy H. Riad; Eslam Hussam; Ahmed M. Gemeay; Ramy A. Aldallal; Ahmed Z.Afify; Fathy H. Riad; Eslam Hussam; Ahmed M. Gemeay; Ramy A. Aldallal; Ahmed Z.Afify

doi:10.3934/mbe.2022309

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6551-6581. doi: 10.3934/mbe.2022309

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Classical and Bayesian inference of the weighted-exponential distribution with an application to insurance data

1.
Mathematics Department, College of Science, Jouf University, P. O.Box 2014, Sakaka, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Minia University, Minia 61519, Egypt
3.
Department of Mathematics, Faculty of science Helwan university, Cairo, Egypt
4.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
5.
College of Business Administration in Hotat bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
6.
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Academic Editor: Jeffrey Yi-Lin Forrest

Received: 11 January 2022 Revised: 13 April 2022 Accepted: 19 April 2022 Published: 26 April 2022

This paper addresses asymmetric flexible two-parameter exponential model called the weighted exponential (WDEx) distribution. Some of its basic mathematical features are evaluated. Its hazard rate accommodates upside-down bathtub, decreasing, decreasing-constant, increasing, and increasing-constant shapes. Five actuarial indicators are studied. We utilize nine classical and Bayesian approaches of estimation for estimating the WDEx parameters. We provide a detailed simulation study to explore and assess the asymptotic behaviors of these estimators. Two approximation methods called the Markov chain Mont Carlo and Tierney and Kadane are applied to obtain the Bayesian estimates. The efficiency and applicability of the WDEx distribution are explored by modeling a lifetime data set from insurance field, showing that the WDEx distribution provides a superior fit over its competing exponential models such as the beta-exponential, Harris extend-exponential, Marshall–Olkin exponential, Marshall–Olkin alpha-power exponential, gamma Weibull, and exponentiated-Weibull distributions.
- exponential distribution,
- risk measures,
- insurance data,
- maximum likelihood estimation,
- Bayes estimation,
- Tierney and Kadane approximation
Citation: Fathy H. Riad, Eslam Hussam, Ahmed M. Gemeay, Ramy A. Aldallal, Ahmed Z.Afify. Classical and Bayesian inference of the weighted-exponential distribution with an application to insurance data[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6551-6581. doi: 10.3934/mbe.2022309

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Abstract

This paper addresses asymmetric flexible two-parameter exponential model called the weighted exponential (WDEx) distribution. Some of its basic mathematical features are evaluated. Its hazard rate accommodates upside-down bathtub, decreasing, decreasing-constant, increasing, and increasing-constant shapes. Five actuarial indicators are studied. We utilize nine classical and Bayesian approaches of estimation for estimating the WDEx parameters. We provide a detailed simulation study to explore and assess the asymptotic behaviors of these estimators. Two approximation methods called the Markov chain Mont Carlo and Tierney and Kadane are applied to obtain the Bayesian estimates. The efficiency and applicability of the WDEx distribution are explored by modeling a lifetime data set from insurance field, showing that the WDEx distribution provides a superior fit over its competing exponential models such as the beta-exponential, Harris extend-exponential, Marshall–Olkin exponential, Marshall–Olkin alpha-power exponential, gamma Weibull, and exponentiated-Weibull distributions.

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