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Title:	Several new models for count data with application in insurance
Authors:	Hossein Zamani Mostafa (P46953)
Supervisor:	Noriszura Ismail, Associate Professor Dr.
Keywords:	Several new models for count data Count data Application in insurance Distribution (Probability theory)
Issue Date:	14-Feb-2012
Description:	Poisson distribution is a standard distribution for modeling count data. However, the mixed distribution is an important approach for obtaining a new probability distribution which provides a more flexible alternative than the Poisson distribution. Therefore, this study introduces a new mixed Poisson distribution, namely the Poisson-weighted exponential, and a new mixed negative binomial distribution, namely the negative binomial-Lindley, which are more flexible than the Poisson distribution and can be used to handle dispersion. Several negative binomial and generalized Poisson regression models such as the negative binomial-1 (NB-1), the negative binomial-2 (NB-2), the generalized Poisson-1 (GP-1) and the generalized Poisson-2 (GP-2) have been fitted for modeling overdispersed or underdispersed count data. However, these regression models are not nested and appropriate statistical tests such as the likelihood ratio test cannot be performed to chose a better model. Hence, this study proposes a new functional form of the generalized Poisson regression model, namely the GP-P model, which can parametrically nests the Poisson, the GP-1 and the GP-2 regression models, and allows the likelihood ratio to be performed to chose a better model. In addition, this study relates the NB-1, the NB-2, the NB-P, the GP-1, the GP-2 and the GP-P regression models through a mean-variance relationship for an easier interpretation and comparison. For several cases, count data often have a large number of zero data than is expected than the Poisson regression model. As an example, motor insurance data often have a large number of zero claims where deductible and no claim discount may increase the number of zero claim data through unreported small claims. The zero inflated Poisson regression model has been suggested for modeling zero-inflated count data. If the count data continue to suggest additional overdispersion, the zero inflated negative binomial-1 (ZINB-1), the zero inflated negative binomial-2 (ZINB-2), the zero inflated generalized Poisson-1 (ZIGP-1) and the zero inflated generalized Poisson-2 (ZIGP-2) regression models have been fitted. However, these regression models are not nested and appropriate statistical tests such as the likelihood ratio test cannot be performed to chose a better model. Therefore, this study suggests a new functional form of the zero inflated generalized Poisson regression model, namely the ZIGP-P model, which can parametrically nests the ZIP, the ZIGP-1 and the ZIGP-2 regression models, and allows the likelihood ratio test to be performed to chose a better model. This study contributes to the statistical and the actuarial literatures through four main aspects; firstly, to introduce a new mixed Poisson distribution, namely the Poisson-weighted exponential distribution, and a new mixed negative binomial distribution, namely the negative binomial-Lindley distribution. Secondly, to propose a new functional form of the generalized Poisson regression model, namely the GP-P model, which parametrically nests the Poisson, the GP-1 and the GP-2 regression models. Thirdly, to relate the NB-1, NB-2, NB-P, GP-1, GP-2 dan GP-P through a mean-variance relationship. Finally, to suggest a new functional form of the zero inflated generalized Poisson regression model, namely the ZIGP-P model, which parametrically nests the ZIP, the ZIGP-1 and the ZIGP-2 regression models.,PhD
Pages:	196
Call Number:	QA273.6 .M665 2012 3
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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