A Novel Model for Quantitative Risk Assessment under Claim-Size Data with Bimodal and Symmetric Data Modeling

Abstract

A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer–von Mises, moments, and Anderson–Darling methods are utilized. For actuarial purposes, a comprehensive simulation study is presented using various combinations to evaluate the performance of the six methods in analyzing insurance risks. These six methods are used in evaluating actuarial risks using insurance claims data. Two applications on bimodal data are presented to highlight the flexibility and relevance of the new distribution. The new distribution is compared to several competing distributions. Actuarial risks are analyzed and evaluated using actuarial data, and the ability to disclose actuarial risks is compared by a comprehensive simulation study, through which actuarial disclosure models are compared using a wide range of well-known models.

Keywords

• actuarial risks
• asymmetric data set
• left skewed claims
• likelihood
• bimodal data
• value-at-risk