A New Compound Lomax Model: Properties, Copulas, Modeling and Risk Analysis Utilizing the Negatively Skewed Insurance Claims Data

Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be "monotonically declining", "symmetric", "bimodal-asymmetric", "asymmetric with right tail", wide peak" or left tail". hazard rate take following shapes: "J-shape", "bathtub (U-shape)", "upside down-increasing", "decreasing-constant", and down-increasing". We use some common copulas, including Farlie-Gumbel-Morgenstern copula, Clayton modified Renyi's copula Ali-Mikhail-Haq present bivariate quasi-Poisson generalized Weibull distributions mathematical modelling. Relevant properties are determined, mean waiting time, deviation, raw incomplete moments, residual life moments reversed life. Two actual data sets examined demonstrate unique extension's usefulness. model provides lowest statistic testing based on two real sets. risk exposure under characterized using five important indicators: value-at-risk, tail variance, tail-value-at-risk, mean-variance, excess loss function. For model, these indicators calculated. In accordance separate indicators, employed analysis. choose focus examining primary since they have straightforward only one peak. All addressed numerical graphical assessment