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This research assesses the performance of over-dispersed Poisson regression model and negative binomial model with count data. It examines the association between price plan features of mobile phone services and the number of people who adopt the plan. Mobile service data is used to estimate the model with a sample of one million customers running from February 2006 to September 2009. Under three main categories, customer type, age, and handset price, we run the model based on price plan features. Estimates are derived from the maximum likelihood estimation (MLE) method. Root mean squared error (RMSE) is used to observe the statistical fits of all the regression models. Then, we construct four estimation and holdout samples, leaving out one, three, six, and twelve months. The estimation constitutes the in-sample (IS) and the holdout represents the out-sample (OS). By estimating the IS, we predict the OS. Root mean squared error of prediction (RMSEP) is checked to see how accurate the prediction is. Results generally suggest that academic year start (AYS), seasonality, duration of months since launch of price plan (DMLP), basic fees, rate with no discount (RND), free call minutes (FCM), free data (FD), free text messaging (FTM), free perk rating (FPR), and handset support all show significant effect. The significance occurs depending on the segment. The RMSE and RMSEP show that the over-dispersed Poisson model outperforms the negative binomial model. Further implications and limitations of the results are discussed. / text

In this thesis, we consider several statistical techniques applicable to claim frequency models of an MTPL portfolio with a focus on overdispersion. The practical part of the work is focused on the application and comparison of the models on real data represented by an MTPL portfolio. The comparison is presented by the results of goodness-of-fit measures. Furthermore, the predictive power of selected models is tested for the given dataset, using the simulation method. Hence, this thesis provides a combination of the analysis of goodness-of-fit results and the predictive power of the models.

Master of Science / Department of Statistics / Wei-Wen Hsu / The zero-inflated Poisson (ZIP) model consists of a Poisson model and a degenerate distribution at zero. Under this model, zero counts are generated from two sources, representing a heterogeneity in the population. In practice, it is often interested to evaluate this heterogeneity is consistent with the observed data or not. Most of the existing methodologies to examine this heterogeneity are often assuming that the Poisson mean is a function of nuisance parameters which are simply the coefficients associated with covariates. However, these nuisance parameters can be misspecified when performing these methodologies. As a result, the validity and the power of the test may be affected. Such impact of misspecification has not been discussed in the literature. This report primarily focuses on investigating the impact of misspecification on the performance of score test for homogeneity in ZIP models. Through an intensive simulation study, we find that: 1) under misspecification, the limiting distribution of the score test statistic under the null no longer follows a chi-squared distribution. A parametric bootstrap methodology is suggested to use to find the true null limiting distribution of the score test statistic; 2) the power of the test decreases as the number of covariates in the Poisson mean increases. The test with a constant Poisson mean has the highest power, even compared to the test with a well-specified mean. At last, simulation results are applied to the Wuhan Inpatient Care Insurance data which contain excess zeros.

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zero-inflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (authors' abstract)

For decades, vehicle time-headway distribution models have been studied by many researchers and traffic engineers. A good time-headway model can be beneficial to traffic studies and management in many aspects; e.g. with a better understanding of road traffic patterns and road user behaviour, the researchers or engineers can give better estimations and predictions under certain road traffic conditions and hence make better decisions on traffic management and control. The models also help us to implement high-quality microscopic traffic simulation studies to seek good solutions to traffic problems with minimal interruption of the real traffic environment and minimum costs. Compared within previously studied models, the mixed (SPM and GQM) mod- els, especially using the gamma or lognormal distributions to describe followers headways, are probably the most recognized ones by researchers in statistical stud- ies of headway data. These mixed models are reported with good fitting results indicated by goodness-of-fit tests, and some of them are better than others in com- putational costs. The gamma-SPM and gamma-GQM models are often reported to have similar fitting qualities, and they often out-perform the lognormal-GQM model in terms of computational costs. A lognormal-SPM model cannot be formed analytically as no explicit Laplace transform is available with the lognormal dis- tribution. The major downsides of using mixed models are the difficulties and more flexibilities in fitting process as they have more parameters than those single models, and this sometimes leads to unsuccessful fitting or unreasonable fitted pa- rameters despite their success in passing GoF tests. Furthermore, it is difficult to know the connections between model parameters and realistic traffic situations or environments, and these parameters have to be estimated using headway samples. Hence, it is almost impossible to explain any traffic phenomena with the param- eters of a model. Moreover, with the gamma distribution as the only common well-known followers headway model, it is hard to justify whether it has described the headway process appropriately. This creates a barrier for better understanding the process of how drivers would follow their preceding vehicles. This study firstly proposes a framework developed using MATLAB, which would help researchers in quick implementations of any headway distributions of interest. This framework uses common methods to manage and prepare headway samples to meet those requirements in data analysis. It also provides common structures and methods on implementing existing or new models, fitting models, testing their performance hence reporting results. This will simplify the development work involved in headway analysis, avoid unnecessary repetitions of work done by others and provide results in formats that are more comparable with those reported by others. Secondly, this study focuses on the implementation of existing mixed models, i.e. the gamma-SPM, gamma-GQM and lognormal-GQM, using the proposed framework. The lognormal-SPM is also tested for the first time, with the recently developed approximation method of Laplace transform available for lognormal distributions. The parameters of these mixed models are specially discussed, as means of restrictions to simplify the fitting process of these models. Three ways of parameter pre-determinations are attempted over gamma-SPM and gamma-GQM models. A couple of response-time (RT) distributions are focused on in the later part of this study. Two RT models, i.e. Ex-Gaussian (EMG) and inverse Gaussian (IVG) are used, for first time, as single models to describe headway data. The fitting performances are greatly comparable to the best known lognormal single model. Further extending this work, these two models are tested as followers headway distributions in both SPM and GQM mixed models. The test results have shown excellent fitting performance. These now bring researchers more alternatives to use mixed models in headway analysis, and this will help to compare the be- haviours of different models when they are used to describe followers headway data. Again, similar parameter restrictions are attempted for these new mixed models, and the results show well-acceptable performance, and also corrections on some unreasonable fittings caused by the over flexibilities using 4- or 5- parameter models.

Várias propostas têm surgido nos últimos anos para problemas que envolvem a predição de observações futuras em modelos mistos, contudo, para os casos em que o problema trata-se em atribuir valores para os efeitos aleatórios de novos grupos existem poucos trabalhos. Tamura, Giampaoli e Noma (2013) propuseram um método que consiste na computação das distâncias entre o novo grupo e os grupos com efeitos aleatórios conhecidos, baseadas nos valores das covariáveis, denominado Método de Predição do Vizinho Mais Próximo ou NNPM (Nearest Neighbors Prediction Method), na sigla em inglês, considerando o modelo logístico misto. O objetivo deste presente trabalho foi o de estender o método NNPM para o modelo Poisson misto, além da obtenção de intervalos de confiança para as predições, para tais fins, foram propostas novas medidas de desempenho da predição e o uso da metodologia Bootstrap para a criação dos intervalos. O método de predição foi aplicado em dois conjuntos de dados reais e também no âmbito de estudos de simulação, em ambos os casos, obtiveram-se bons desempenhos. Dessa forma, a metodologia NNPM apresentou-se como um método de predição muito satisfatório também no caso Poisson misto. / Many proposals have been created in the last years for problems in the prediction of future observations in mixed models, however, there are few studies for cases that is necessary to assign random effects values for new groups. Tamura, Giampaoli and Noma (2013) proposed a method that computes the distances between a new group and groups with known random effects based on the values of the covariates, named as Nearest Neighbors Prediction Method (NNPM), considering the mixed logistic model. The goal of this dissertation was to extend the NNPM for the mixed Poisson model, in addition to obtaining confidence intervals for predictions. To attain such purposes new prediction performance measures were proposed as well as the use of Bootstrap methodology for the creation of intervals. The prediction method was applied in two sets of real data and in the simulation studies framework. In both cases good performances were obtained. Thus, the NNPM proved to be a viable prediction method also in the mixed Poisson case.

Várias propostas têm surgido nos últimos anos para problemas que envolvem a predição de observações futuras em modelos mistos, contudo, para os casos em que o problema trata-se em atribuir valores para os efeitos aleatórios de novos grupos existem poucos trabalhos. Tamura, Giampaoli e Noma (2013) propuseram um método que consiste na computação das distâncias entre o novo grupo e os grupos com efeitos aleatórios conhecidos, baseadas nos valores das covariáveis, denominado Método de Predição do Vizinho Mais Próximo ou NNPM (Nearest Neighbors Prediction Method), na sigla em inglês, considerando o modelo logístico misto. O objetivo deste presente trabalho foi o de estender o método NNPM para o modelo Poisson misto, além da obtenção de intervalos de confiança para as predições, para tais fins, foram propostas novas medidas de desempenho da predição e o uso da metodologia Bootstrap para a criação dos intervalos. O método de predição foi aplicado em dois conjuntos de dados reais e também no âmbito de estudos de simulação, em ambos os casos, obtiveram-se bons desempenhos. Dessa forma, a metodologia NNPM apresentou-se como um método de predição muito satisfatório também no caso Poisson misto. / Many proposals have been created in the last years for problems in the prediction of future observations in mixed models, however, there are few studies for cases that is necessary to assign random effects values for new groups. Tamura, Giampaoli and Noma (2013) proposed a method that computes the distances between a new group and groups with known random effects based on the values of the covariates, named as Nearest Neighbors Prediction Method (NNPM), considering the mixed logistic model. The goal of this dissertation was to extend the NNPM for the mixed Poisson model, in addition to obtaining confidence intervals for predictions. To attain such purposes new prediction performance measures were proposed as well as the use of Bootstrap methodology for the creation of intervals. The prediction method was applied in two sets of real data and in the simulation studies framework. In both cases good performances were obtained. Thus, the NNPM proved to be a viable prediction method also in the mixed Poisson case.

La présente thèse vise à explorer différents types de modèles log-bilinéaires dans le domaine des sciences actuarielles. Le point de départ consiste en le modèle de Lee-Carter, utilisé pour les problèmes de projection de la mortalité. Différentes variantes sont développées, et notamment le modèle de Poisson log-bilinéaire. L'introduction de variables explicatives est également analysée. Enfin, une tentative de d'exportation de ces modèles au cas des triangles IBNR est effectuée.