A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting

Heba Soltan Mohamed; Gauss M Cordeiro; R Minkah; Haitham M Yousof; Mohamed Ibrahim

doi:10.1080/02664763.2022.2125936

A size-of-loss model for the negatively skewed insurance claims data: applications, risk analysis using different methods and statistical forecasting

J Appl Stat. 2022 Sep 21;51(2):348-369. doi: 10.1080/02664763.2022.2125936. eCollection 2024.

Authors

Heba Soltan Mohamed¹, Gauss M Cordeiro², R Minkah³, Haitham M Yousof⁴, Mohamed Ibrahim⁵

Affiliations

¹ Department of Statistics and Quantitative Methods, Faculty of Business Administration, Horus University, Damietta, Egypt.
² Departamento de Estatistica, Universidade Federal de Pernambuco, Recife, Brazil.
³ Department of Statistics and Actuarial Science, School of Physical and Mathematical Sciences, College of Basic and Applied Sciences, University of Ghana, Accra, Ghana.
⁴ Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt.
⁵ Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt.

Abstract

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered.

Keywords: 60E05; 62E10; 62F10; 62F15; 62H05; 62P05; Autoregressive model; Cullen and Frey plot; claims payment; mean-of-order-p; peaks-over random threshold; risk analysis.