Noriszura Ismail

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.

Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events

The two primary approaches of extreme events analysis are annual maximum series (AMS), which fits Generalized Extreme Value (GEV) distribution to the yearly peaks of events in the observation period, and partial duration series (PDS), which fits Generalized Pareto (GP) distribution to the peaks of events that exceed a given threshold. The PDS is able to reduce sampling uncertainty and is more useful in dealing with extreme values and asymmetries in the tails, but the optimal threshold is required. The objective of this study is to compare and determine the best method for selecting the optimal threshold of PDS using the hourly, 12-h and 24-h aggregated data of rainfall time series in Peninsular Malaysia. The choice of the threshold, or the number of largest order statistics, can be estimated by the parameters of extreme events. In this study, thirteen semi-parametric estimators are considered and applied to estimate the shape parameter or extreme value index (EVI). A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. Based on the smallest MSE, the majority of stations and data durations favor the Adapted Hill estimator, followed by the QQ, Hill and Moment Ratio 1 estimators. Therefore, this study proves that the application of different estimators on real data may result in different optimal values of threshold and the choice of the best method is very much data-dependent.

Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events

Analysis of extreme rainfall events can be performed using two main approaches; fitting Generalized Extreme Value distribution to the yearly peaks of events in the observation period or the annual maximum series, and fitting Generalized Pareto distribution to the peaks of events that exceed a given threshold or the partial duration series. Even though partial duration series are able to reduce sampling uncertainty and are useful for analyzing extreme values and tail asymmetries, the series require an optimal threshold. The objective of this study is to compare and determine the best method for selecting the optimal threshold of partial duration series using hourly, 12-hour and 24-hour data of rainfall time series in Peninsular Malaysia. Nine semi-parametric second order reduced-bias estimators are applied to estimate extreme value index and six estimators are used for the external estimation of the second order parameter. A semi-parametric bootstrap is used to estimate mean square error of the estimator at each threshold and the optimal threshold is then selected based on the smallest mean square error. Based on the plots of extreme value index and mean square error, several second order reduced-bias estimators behave reasonably well compared to Hill estimator, as indicated by their stable sample paths and flatter mean square errors.

Bivariate zero-inflated negative binomial regression model with applications

ABSTRACT Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.

Insolvency prediction model using artificial neural network for Malaysian general insurers

Insolvency of insurance companies has been a concern to the community due to the need to protect the general public from the aftermath of insurer insolvency and to try to minimize the costs associated to this difficulty such as the insurance guaranty funds. The artificial neural network is utilized in this study to create an insolvency predictive model that could predict any future failure of general insurance company in Malaysia. The neural networks results show high predictability, suggesting the usefulness of this method for predicting future insurer insolvency in Malaysia.

Evaluating the effects of road geometry, environment, and traffic volume on rollover crashes

There are a number of factors that cause motor vehicles to rollover. However, the impacts of roadway characteristics on rollover crashes have rarely been addressed in the literature. This study aims to apply a set of crash prediction models in order to estimate the number of rollovers as a function of road geometry, the environment, and traffic conditions. To this end, seven count-data models, including Poisson (PM), negative binomial (NB), heterogeneous negative binomial (HTNB), zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), hurdle Poisson (HP), and hurdle negative binomial (HNB) models, were developed and compared using crash data collected on 448 segments of Malaysian federal roads. The results showed that the HTNB was the best-fit model among the others to model the frequency of rollovers. The variables Light-Vehicle Traffic (LVT), horizontal curvature, access points, speed limit, and centreline median were positively associated with the crash frequency, while UnPaved Shoulder Width (UPSW) and Heavy-Vehicle Traffic (HVT) were found to have the opposite effect. The findings of this study suggest that rollovers could potentially be reduced by developing road safety countermeasures, such as access management of driveways, straightening sharp horizontal curves, widening shoulder width, better design of centreline medians, and posting lower speed limits and warning signs in areas with higher rollover tendency.

Projection of retirement adequacy using wealth-need ratio: A case study in Malaysia

Adequacy of retirement income is very important to maintain a comfortable living standard during retirement. Under a life cycle model, assets are mainly accumulated during an individual’s work life to finance consumption after retirement. A generally accepted goal of retirement planning is to provide enough income during retirement to prevent the level of living from dropping much below the pre-retirement level. Retirement wealth can be defined as adequate if the total retirement income is equal or greater than the desired total retirement consumption (or needs). In this study, retirement adequacy is projected using the Malaysian Household Income Survey (HIS) 2009 data which is based on 5881 sample of households and contains information on income, demographic and socioeconomic status of each household. Besides the projection of retirement adequacy, a regression of the ratio of projected wealth to needs (or wealth-needs ratio) is performed to investigate the demographic and socioeconomic determinants of retirement adequacy in Malaysia. The results show that 69% of households in Malaysia are adequately prepared for retirement.Adequacy of retirement income is very important to maintain a comfortable living standard during retirement. Under a life cycle model, assets are mainly accumulated during an individual’s work life to finance consumption after retirement. A generally accepted goal of retirement planning is to provide enough income during retirement to prevent the level of living from dropping much below the pre-retirement level. Retirement wealth can be defined as adequate if the total retirement income is equal or greater than the desired total retirement consumption (or needs). In this study, retirement adequacy is projected using the Malaysian Household Income Survey (HIS) 2009 data which is based on 5881 sample of households and contains information on income, demographic and socioeconomic status of each household. Besides the projection of retirement adequacy, a regression of the ratio of projected wealth to needs (or wealth-needs ratio) is performed to investigate the demographic and socioeconomic determinants of re...

Development of car theft crime index in peninsular Malaysia

Vehicle theft is classified as property crime and is considered as the most frequently reported crime in Malaysia. The rising number of vehicle thefts requires proper control by relevant authorities, especially through planning and implementation of strategic and effective measures. Nevertheless, the effort to control this crime would be much easier if there is an indication or index which is more specific to vehicle theft. This study aims to build an index crime which is specific to vehicle theft. The development of vehicle theft index proposed in this study requires three main steps; the first involves identification of criteria related to vehicle theft, the second requires calculation of degrees of importance, or weighting criteria, which involves application of correlation and entropy methods, and the final involves building of vehicle theft index using method of linear combination, or weighted arithmetic average. The results show that the two methods used for determining weights of vehicle theft inde...