Abstract
A new, flexible claim-size Chen density is derived for modeling asymmetric data (negative and positive) with different types of kurtosis (leptokurtic, mesokurtic and platykurtic). The new function is used for modeling bimodal asymmetric medical data, water resource bimodal asymmetric data and asymmetric negatively skewed insurance-claims payment triangle data. The new density accommodates the “symmetric”, “unimodal right skewed”, “unimodal left skewed”, “bimodal right skewed” and “bimodal left skewed” densities. The new hazard function can be “decreasing–constant–increasing (bathtub)”, “monotonically increasing”, “upside down constant–increasing”, “monotonically decreasing”, “J shape” and “upside down”. Four risk indicators are analyzed under insurance-claims payment triangle data using the proposed distribution. Since the insurance-claims data are a quarterly time series, we analyzed them using the autoregressive regression model AR(1). Future insurance-claims forecasting is very important for insurance companies to avoid uncertainty about big losses that may be produced from future claims.
Highlights
Introduction and MotivationProbability-based distributions can provide adequate descriptions of exposure to risk.According to [1], the number of exposure is a function often called key risk indicators (RIs).Such RIs inform risk managers and actuaries about the degree to which their company is subject to aspects of risk
The new model was motivated by its wide applicability in modeling “unimodal rightskewed”, “unimodal left-skewed”, “bimodal right-skewed” and “bimodal left-skewed”
Relevant statistical properties of the novel model were derived such as conditional moments, mean residual life and mean past lifetime
Summary
Probability-based distributions can provide adequate descriptions of exposure to risk. According to [1], the number of exposure is a function often called key risk indicators (RIs). Such RIs inform risk managers and actuaries about the degree to which their company is subject to aspects of risk. Some of RIs such as VaR, TVaR, TV and TMV (see [7]) are considered for the left-skewed insurance-claims data under a new model called the exponentiated Weibull Chen (EWC) model. The claim process involves, usually, two independent random variables (RVs): the first one is the claim-size RV, and other is the claim-count RV These two RVs can be combined to create a third RV called the aggregate-loss RV. The abovementioned RIs are analyzed under the insurance-claims payment triangle data using the EWC distribution
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