Hossein Zamani

Score test for testing zero-inflated Poisson regression against zero-inflated generalized Poisson alternatives

In several cases, count data often have excessive number of zero outcomes. This zero-inflated phenomenon is a specific cause of overdispersion, and zero-inflated Poisson regression model (ZIP) has been proposed for accommodating zero-inflated data. However, if the data continue to suggest additional overdispersion, zero-inflated negative binomial (ZINB) and zero-inflated generalized Poisson (ZIGP) regression models have been considered as alternatives. This study proposes the score test for testing ZIP regression model against ZIGP alternatives and proves that it is equal to the score test for testing ZIP regression model against ZINB alternatives. The advantage of using the score test over other alternative tests such as likelihood ratio and Wald is that the score test can be used to determine whether a more complex model is appropriate without fitting the more complex model. Applications of the proposed score test on several datasets are also illustrated.

Functional Form for the Generalized Poisson Regression Model

This article develops a functional form of the generalized Poisson regression model that parametrically nests the Poisson and the two well known generalized Poisson regression models (GP-1 and GP-2). The proposed model is applied on the Malaysian motor insurance claim count data.

Functional Form for the Zero-Inflated Generalized Poisson Regression Model

The generalized Poisson (GP) regression is an increasingly popular approach for modeling overdispersed as well as underdispersed count data. Several parameterizations have been performed for the GP regression, and the two well known models, the GP-1 and the GP-2, have been applied. The GP-P regression, which has been recently proposed, has the advantage of nesting the GP-1 and the GP-2 parametrically, besides allowing the statistical tests of the GP-1 and the GP-2 against a more general alternative. In several cases, count data often have excessive number of zero outcomes than are expected in the Poisson. This zero-inflation phenomenon is a specific cause of overdispersion, and the zero-inflated Poisson (ZIP) regression model has been proposed. However, if the data continue to suggest additional overdispersion, the zero-inflated negative binomial (ZINB-1 and ZINB-2) and the zero-inflated generalized Poisson (ZIGP-1 and ZIGP-2) regression models have been considered as alternatives. This article proposes a functional form of the ZIGP which mixes a distribution degenerate at zero with a GP-P distribution. The suggested model has the advantage of nesting the ZIP and the two well known ZIGP (ZIGP-1 and ZIGP-2) regression models, besides allowing the statistical tests of the ZIGP-1 and the ZIGP-2 against a more general alternative. The ZIP and the functional form of the ZIGP regression models are fitted, compared and tested on two sets of count data; the Malaysian insurance claim data and the German healthcare data.

Bivariate Poisson-weighted exponential distribution with applications

This paper proposes the bivariate version of Poisson-weighted exponential (PWE) distribution considered in Zamani and Ismail (2010). This new discrete bivariate Poisson-weighted exponential (BPWE) distribution can be used as an alternative for modeling dependent and over-dispersed count data. Several properties such as mean, variance, correlation and joint moment generating function of the new BPWE distribution are discussed. A numerical example is given and the BPWE distribution is compared to bivariate Poisson (BP) distribution. The results show that BPWE distribution provides larger log likelihood and smaller AIC, indicating that BPWE distribution is better than BP distribution and can be used as an alternative for fitting dependent and over-dispersed count data.

Score test for testing Poisson regression against generalized Poisson alternatives

Poisson regression model has been considered as a standard method for modeling count data. However, count data often display overdispersion, and thus, negative binomial (NB) regression model has been suggested for handling overdispersed count data. In addition, generalized Poisson (GP) regression model has been proposed for handling both over- and underdispersed count data. This study proposes the score test for testing Poisson regression against GP alternatives and proves that it is equal to the score test for testing Poisson regression against NB alternatives. The advantage of score test over other alternative tests such as likelihood ratio and Wald is that the score test can be used to determine whether a more complex model is appropriate without fitting the more complex model. Application of the proposed score test on the Malaysian private car claim count data is illustrated.

Estimation of count data using mixed Poisson, generalized Poisson and finite Poisson mixture regression models

This study relates the Poisson, mixed Poisson (MP), generalized Poisson (GP) and finite Poisson mixture (FPM) regression models through mean-variance relationship, and suggests the application of these models for overdispersed count data. As an illustration, the regression models are fitted to the US skin care count data. The results indicate that FPM regression model is the best model since it provides the largest log likelihood and the smallest AIC, followed by Poisson-Inverse Gaussion (PIG), GP and negative binomial (NB) regression models. The results also show that NB, PIG and GP regression models provide similar results.

Poisson-weighted Lindley distribution and its application on insurance claim data

This paper introduces a new two-parameter mixed Poisson distribution, namely the Poisson-weighted Lindley (P-WL), which is obtained by mixing the Poisson with a new class of weighted Lindley distributions. The closed form, the moment generating function and the probability generating function are derived. The parameter estimations methods of moments and the maximum likelihood procedure are provided. Some simulation studies are conducted to investigate the performance of P-WL distribution. In addition, the compound P-WL distribution is derived and some applications to insurance area based on observations of the number of claims and on observations of the total amount of claims incurred will be illustrated.