Open Access Journal Article

A simulation study on the insurance claims distribution using Weibull distribution

by Hamza Abubakar a,* orcid  and  Muhammad Lawal Danrimi b orcid
a
Department of Mathematics, Isa Kaita College of Education, Katsina State, Nigeria
b
Department of Accounting, Umaru Musa Yar’adua University, Katsina State, Nigeria
*
Author to whom correspondence should be addressed.
EAL  2023, 34; 2(3), 34; https://doi.org/10.58567/eal02030008
Received: 26 February 2023 / Accepted: 8 July 2023 / Published Online: 17 July 2023
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Abstract

The Weibull distribution is extensively useful in the field of finance, insurance and natural disasters. Recently, It has been considered as one of the most frequently used statistical distributions in modelling and analyzing stock pricing movement and uncertain prediction in financial and investment data sets, such as insurance claims distribution. It is well known that the Bayes estimators of the two-parameter Weibull distribution do not have a compact form and the closed-form expression of the Bayes estimators cannot be obtained. In this paper and the Bayesian setting, it is assumed that the scale parameter of the Weibull model has a gamma prior under the assumption that its shape parameter is known. A simulation study is performed using random claims amount to compare the performance of the Bayesian approach with traditional maximum likelihood estimators in terms of Root Mean Square Errors (RMSE) and Mean Absolute Error (MAE) for different sample sizes, with specific values of the scale parameter and shape parameters. The results have been compared with the estimated result via the maximum likelihood method. The result revealed that the Bayesian approach behaves similarly to the maximum likelihood method when the sample size is small. Nevertheless, in all cases for both methods, the RMSE and MAE decrease as the sample size increases. Finally, applications of the proposed model to the insurance claim data set have been presented.

Keywords: Weibull distribution; Bayesian estimator; maximum likelihood estimator; Insurance claim;
Copyright: © 2023 by Abubakar and Danrimi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (Creative Commons Attribution 4.0 International License). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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ACS Style
Abubakar, H.; Danrimi, M. L. A simulation study on the insurance claims distribution using Weibull distribution. Economic Analysis Letters, 2023, 2, 34. https://doi.org/10.58567/eal02030008
AMA Style
Abubakar H, Danrimi M L. A simulation study on the insurance claims distribution using Weibull distribution. Economic Analysis Letters; 2023, 2(3):34. https://doi.org/10.58567/eal02030008
Chicago/Turabian Style
Abubakar, Hamza; Danrimi, Muhammad L. 2023. "A simulation study on the insurance claims distribution using Weibull distribution" Economic Analysis Letters 2, no.3:34. https://doi.org/10.58567/eal02030008
APA style
Abubakar, H., & Danrimi, M. L. (2023). A simulation study on the insurance claims distribution using Weibull distribution. Economic Analysis Letters, 2(3), 34. https://doi.org/10.58567/eal02030008

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