Regression in the Bivariate Poisson Distribution

Kocherlakota, S.; Kocherlakota, Kathleen

doi:10.1081/sta-100002259

Cited by 61 publications

(35 citation statements)

References 2 publications

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“…Jung and Winkelmann (1993) introduced and implemented bivariate Poisson regression model using a Newton-Raphson procedure. Ho and Singer (2001) and Kocherlakota and Kocherlakota (2001) proposed a generalized least squares and Newton Raphson algorithm for maximizing the log-likelihood respectively. Here we construct an EM algorithm to remedy convergence problems encountered with the Newton Raphson procedure.…”

Section: Models For Bivariate Poisson Data 21 Bivariate Poisson Regmentioning

confidence: 99%

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models inR

Karlis¹,

Ntzoufras²

2005

J. Stat. Soft.

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In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using bivpois package is provided.

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Section: Models For Bivariate Poisson Data 21 Bivariate Poisson Regmentioning

confidence: 99%

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models inR

Karlis¹,

Ntzoufras²

2005

J. Stat. Soft.

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“…One popular bivariate Poisson distribution proposed by Kocherlakota and Kocherlakota described in Kocherlakota and Kocherlakota (2001) discussed in below. Let, the n independent observations y 1 , y 2 , .…”

Section: The Bivariate Poisson Modelmentioning

confidence: 98%

“…Simulation study has been performed for some specific probability models involving AR (1) and exchangeable structure. Performance of the estimates has been looked into by comparing the proposed method with existing GEE method and bivariate Poisson model proposed by Kocherlakota and Kocherlakota (2001). We have illustrated the application of the proposed model employing the Health and Retirement Study (HRS) data (Health andRetirement Study 1992[2004]) on divorce among elderly people in the USA.…”

Section: Introductionmentioning

confidence: 98%

A conditional count model for repeated count data and its application to GEE approach

Dey

Islam

2015

Stat Papers

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In this article, a conditional model is proposed for modeling longitudinal count data. The joint density is disintegrated into the marginal and conditional densities according to the multiplication rule. It allows both positive and negative correlation among variables, which most multivariate count models do not possess. To show the efficiency of the proposed model for count data, we have applied to the generalized estimating equations and the inverse Fisher information matrix is compared with the covariance matrix from estimating equations. A simulation experiment is displayed and an application of the model to divorce data is presented. In addition, a comparison of conditional model and bivariate Poisson model proposed by Kocherlakota and Kocherlakota has shown using simulated data.

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“…Different algorithms have been provided to implement bivariate Poisson regression models (Ho and Singer, 2001;Kocherlakota and Kocherlakota, 2001; or adopting a Bayesian point of view, Tsionas, 2001;Karlis and Meligkotsidou, 2005). Here an EM algorithm provided by Karlis and Ntzoufras (2005) and its implementation using R (bivpois package) is used.…”

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confidence: 99%

A Priori Ratemaking Using Bivariate Poisson Regression Models

Bermúdez

2008

SSRN Journal

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In automobile insurance, it is useful to achieve a priori ratemaking by resorting to generalized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper examines an a priori ratemaking procedure when including two different types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tariff system might be affected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

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Regression in the Bivariate Poisson Distribution

Cited by 61 publications

References 2 publications

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models inR

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models inR

A conditional count model for repeated count data and its application to GEE approach

A Priori Ratemaking Using Bivariate Poisson Regression Models

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