Zero-Inflated Poisson Regression Analysis On Frequency Of Health Insurance Claim PT. XYZ

Abstract

Modeling data count is an important thing in various fields. For this purpose, Poisson regression models are often used. However, in this model there is an assumption of equidispersion data where the mean value equals the value of the variance. In fact, this assumption is often violated in the observed data. In real data, the value of variance actually exceeds the mean (overly dispersed) value with the cause of the overdispersion depending on many situations. When the overdispersion source is exceeds zero (excess zero), then a more suitable model to use is the Zero-inflated Poisson regression model. In this paper, after the framework of Poisson regression and the Zero-inflated Poisson regression is reviewed then the model is adjusted to the claim frequency data in a private health insurance scheme where the frequency of claims is overly dispersed because of the number of zeros in the data set. Then Vuong's test is done to compare the two models and obtain the result that the Zero-inflated Poisson regression is more suitable for modeling the frequency data of PT.

Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

“…, J; n 0 is the number of observed zeros; and J j=0 n j = n is the total number of observations or the sample size. Based on log-likelihood function (13), maximum likelihood estimates ω, p, and ˆ are the roots of equations ∂l ∂ω = 0, ∂l ∂p = 0, and ∂l ∂θ = 0, respectively. Here, we have…”

“…Iwunor [12] studied the number of male rural migrants from households by using an inflated geometric distribution and estimated the parameters of the latter; the results show that the maximum likelihood estimates were not too different from the method of moments values. Kusuma et al [13] showed that a ZIP regression model is more suitable than an ordinary Poisson regression model for modeling the frequency of health insurance claims.…”

The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

“…When analyzing natural resources, Lee and Kim [5] recommended a ZIP model from a practical viewpoint for the number of torrential rainfall occurrences at the Daegu and Busan rain gauges in South Korea and compared it with the Poisson distribution, the generalized Poisson distribution (GPD), and the ZI generalized Poisson (ZIGP), and the Bayesian ZIGP model. In the field of insurance, Boucher et al [6] adopted a ZIP distribution model for analyzing insurance data, while Kusuma and Purwono [7] showed that a ZIP regression model is more suitable than an ordinary Poisson regression model for modeling the frequency data of claims from the health insurance company PT.XYZ.…”