Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in<i>R</i>

Karlis, Dimitris; Ntzoufras, Ioannis

doi:10.18637/jss.v014.i10

Cited by 90 publications

(98 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(a) Karlis & Ntzoufras [18] considered two regression models to fit the data; i.e., bivariate Poisson The estimates of parameters for first four models are reported in the second column of Table 7. The values of AIC and BIC based on the Total Likelihood Function are summarized in the last two columns of Table 7.…”

Section: Model Comparisonmentioning

confidence: 99%

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

View full text Add to dashboard Cite

To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP) distributions by incorporating a multiplicative factor (or dependency parameter) λ, named as Type I and Type II bivariate ZIGP λ distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over-or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP λ share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP λ have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

show abstract

Section: Model Comparisonmentioning

confidence: 99%

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

View full text Add to dashboard Cite

show abstract

“…Bohning et al, 1999) that zero-inflated Poisson models are overdispersed relative to simple Poisson models. In the bivariate (multivariate case) it has been shown that the covariance also increases (see, Wang et al, 2003 andNtzoufras, 2005). Hence, inflated models can introduce improvements in several aspects of the data.…”

Section: Zero-inflated Modelsmentioning

confidence: 99%

Modelling Dependence in a Ratemaking Procedure with Multivariate Poisson Regression Models

Bermúdez

Karlis

2010

SSRN Journal

Self Cite

View full text Add to dashboard Cite

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different multivariate Poisson regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to date, mainly because of their computational difficulties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

show abstract

“…However, here we follow the zero-inflated bivariate Poisson model proposed by Karlis and Ntzoufras (2005). In fact, they propose an extension of the simple zero-inflated model which inflates the probabilities in the diagonal of the probability table.…”

mentioning

confidence: 99%

“…Here an EM algorithm provided by Karlis and Ntzoufras (2005) and its implementation using R (bivpois package) is used. Standard errors for the parameter estimates are calculated using standard bootstrap methods (boot package in R).…”

mentioning

confidence: 99%

A Priori Ratemaking Using Bivariate Poisson Regression Models

Bermúdez

2008

SSRN Journal

View full text Add to dashboard Cite

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.

show abstract

Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models inR

Cited by 90 publications

References 26 publications

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Modelling Dependence in a Ratemaking Procedure with Multivariate Poisson Regression Models

A Priori Ratemaking Using Bivariate Poisson Regression Models

Contact Info

Product

Resources

About