Estimation of Claim Cost Data Using Zero Adjusted Gamma and Inverse Gaussian Regression Models

Abstract

In actuarial and insurance literatures, several researchers suggested generalized linear regression models (GLM) for modeling claim costs as a function of risk factors. The modeling of claim costs involving both zero and positive claims experience has been carried out by fitting the claim costs collectively using Tweedie model. However, the probability of zero claims in Tweedie model is not allowed to be fitted explicitly as a function of explanatory variables. The purpose of this article is to propose the application of Zero Adjusted Gamma (ZAGA) and Zero Adjusted Inverse Gaussian (ZAIG) regression models for modeling both zero and positive claim costs data. The models are fitted to the Malaysian motor insurance claims experiences which are divided into three types namely Third Party Bodily Injury (TPBI), Own Damage (OD) and Third Party Property Damage (TPPD). The fitted models show that both claim probability and claim cost are affected by either the same or different explanatory variables. The fitted models also allow the relative risk of each rating factor to be compared and the low or high risk vehicles to be identified, not only for the claim cost but also for the claim probability. The AIC and BIC indicate that ZAIG regression is the best model for modeling both positive and zero claim costs for all claim types

Modern claim frequency and claim severity models: An application to the Russian motor own damage insurance market

“…In order to be consistent with the usage of the Gamma distribution, we ran a formal test of average claim size fit for the Gamma-distribution (Villaseñor & González-Estrada, 2015). With the test statistic V = 2.076 and the p-value = 0.142, we do not reject the null hypothesis that the Gamma-distribution is well suited for the average claim size variable, which is in line with the modern literature (Resti, Ismail, & Jamaan, 2013). …”

Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya

“…Claims were predicted for a period of 24 weeks (8 months). The maximum and minimum predicted claims were six (7) and zero (0) respectively. Hence at any expected time the insurer would expect a maximum of seven (7) claims and a minimum of zero (0) claims.…”

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A New Mixture of Exponential-Gamma Distribution

“…In this section, we carry out simulation study to examine the performance and accuracy of the Maximum Likelihood Estimates (MLEs) of the NMEG distribution. In each simulation, 10,000 samples of sizes 50, 75, 100,150 and 200 n  were generated for different values of the parameters  and  using the quantile function of the NMEG distribution in equation (15). For each sample, the MLEs are obtained, these are used to compute values of the following quantities with the help of R package.…”