An Alternative Type II Claims Pareto Model for Reliability and Bimodal Risk Analysis: Copulas, Properties, Mathematical Modeling, and Actuarial Case Study

This article aims to present a new type-II claims Pareto extension for statistical reliability and actuarial analysis. The new probabilistic density can be simplified in terms of the baseline densities. Some new bivariate types were developed under some copula approaches. Many important statistical and mathematical properties that serve the study have been derived including the concavity and convexity. For statistical modeling in the field of engineering and reliability, the new distribution was applied to measure the durability of aircraft windshields. The new type-II claims Pareto distribution is analyzed with a comprehensive comparison with many different Pareto type-II extensions, such as those obtained from the Topp–Leone, beta, Kumaraswamy, odd log-logistic, and gamma families. As for the statistical analysis of risks considering bimodal insurance claims data, an integrated case study was presented in which we used some important and effective indicators in measuring and analyzing risks considering the new probability distribution. Statistical risk analysis was conducted considering a variety of confidence levels (60%,70%,80%,90%,95% and 99%.) to provide a broader analytical framework for insurance companies that prefer more conservative policies in maintaining reserves in order to meet bimodal insurance claims. In the same context, we presented a comprehensive graphical simulation study (in terms of biases and mean squared errors) to measure and evaluate the behavior of the estimators of the maximum likelihood method due to its use in all types of statistical analysis in this work.