A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data


  • Hamza Abubakar 1) School of Mathematical Sciences, University of Science Malaysia, Malaysia 2) Department of Mathematics, Isa Kaita College of Education, Dutsin-Ma, Katsina, Nigeria
  • Shamsul Rijal Muhammad Sabri School of Mathematical Sciences, University of Science Malaysia, Malaysia




Weibull distribution, Bayesian method, simulated annealing, maximum likelihood Insurance claim, actuarial measures


Statistical distributions are of great interest for actuaries in modelling and fitting the distribution of various data sets. It can be used to present a description of risk exposure on the investment, where the level of exposure to the risk can be determined by “key risk indicators” that usually are functions of the statistical model. Financial mathematicians and actuarial scientists often use such key risk indicators to determine the degree to which a particular company is subject to certain aspects of risk, which arise from changes in underlying variables such as prices of equity, interest rates fluctuations, or exchange rates. Weibull distribution is one of the most popular statistical distribution models employed by the actuarial and financial risk management problems in fitting and or in modelling the behaviours of financial data or lifetime event data to forecast stock pricing movement or uncertainly prediction. In this study, a Bayesian approach to the Weibull distribution model on the assumption of gamma prior to Weibull distribution parameters has been proposed. A computational study based on the actuarial measures is conducted, proving the proposed distribution of the claim amount. Along this line, in assessing the performance of the proposed method, the results of the simulations study have been conducted to explore the efficiency of the proposed estimators is compared to a maximum likelihood (MLE) and simulated annealing algorithm (SA). Finally, an actuarial real data set is analyzed, proving that the proposed model can be used effectively to model insurance claim data.


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Author Biographies

Hamza Abubakar, 1) School of Mathematical Sciences, University of Science Malaysia, Malaysia 2) Department of Mathematics, Isa Kaita College of Education, Dutsin-Ma, Katsina, Nigeria

Hamza Abubakar received both his B.Sc. in Mathematics and MSc in Financial Mathematics from the University of Abuja, Nigeria in 2006 and 2015 respectively. He holds a PhD degree in Financial Mathematics from the University of Sciences Malaysia. Hamza joined the service of Isa Kaita College of Education, Dutsin-ma, Katsina, Nigeria in 2008 and was promoted to the rank of Senior Lecturer. He is an active member of the Nigerian Mathematical Society, the Mathematical Association of Nigeria, the Science Teachers Association of Nigeria, and the International Association of Engineers (OR and AI). His research interests include Financial Mathematics, neural network modeling, and metaheuristics optimization.

Shamsul Rijal Muhammad Sabri, School of Mathematical Sciences, University of Science Malaysia, Malaysia

Shamsul Rijal Muhammad Sabri received both his B.Sc. in Actuarial Science and MSc in Statistics from the National University of Malaysia in the year 1998 and 2001 respectively. He then received PhD degree in Applied Statistics from the University Malaya in the year 2009. Shamsul Rijal is currently serving with the School of Mathematical Sciences, University of Science, Malaysia. He is an active member of the Malaysian Mathematical Sciences Society (PERSAMA). His research interests include Financial Mathematics, Statistical Modelling and Simulation studies.


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How to Cite

Abubakar, H. ., & Sabri, S. R. M. . (2023). A Bayesian Approach to Weibull Distribution with Application to Insurance Claims Data. Journal of Reliability and Statistical Studies, 16(01), 1–24. https://doi.org/10.13052/jrss0974-8024.1611