Bayesian predictive analysis for Weibull-Pareto composite model with an application to insurance data

Abstract

Aminzadeh and Deng, respectively provide Bayesian predictive models for Exponential-Pareto and Inverse Gamma-Pareto composite distributions which are one-parameter models. The purpose of this article is to develop an alternative Bayesian predictive model (two-parameter) which can be used to compute important risk measures that are not defined via the above predictive models. Bayesian predictive density for the Weibull-Pareto composite distribution is developed and is used to compute risk measures such as Value at Risk (VaR), Conditional Tail Expectation (CTE), Predictive Expectation (PE), Limited Predictive Expected value (LPE), Limited Predictive Variance (LPV), and Limited Predictive Tail-VaR (LPCTE). Accuracy of parameter estimates as well as the risk measures are assessed via simulation studies. It is shown that the informative Bayes estimates are consistently more accurate than ML and the non-informative Bayes estimates. Backtesting for the risk measures is performed and goodness-of-fit of Weibull-Pareto among other composite models to the Danish fire data is assessed.