An extended Rayleigh Weibull model with actuarial measures and applications

In this article, we discuss a new extension of the Rayleigh-Weibull model using the Marshall-Olkin family of distributions. The proposed model is called the Marshall-Olkin-Rayleigh-Weibull (MORW) model. Various statistical properties of the MORW distribution are discussed, including explicit expressions for quantiles, moments, incomplete and conditional moments, some inequality measures, moment generating function, moments of the residual and reversed residual life, the Rényi entropy, and order statistics. Six different estimation methods are considered to investigate the behavior of the model parameters within the MORW model. A Monte Carlo simulation study is conducted to evaluate the performance of these different estimators. In addition, some actuarial measures, such as the Value-at-Risk, the expected shortfall, the tail Value-at-Risk, the tail variance, the tail variance premium, the tail conditional expectation, and the tail standard deviation premium, are calculated. Finally, applying the model to real data sets illustrates the applicability and usefulness of the MORW distribution.