A bivariate Poisson count data model using conditional probabilities

Berkhout, Peter; Plug, Erik

doi:10.1111/j.1467-9574.2004.00126.x

Cited by 64 publications

(69 citation statements)

References 13 publications

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“…We show, in this work, that the φ-divergence from model of Berkhout et al (2004) to model of Holgate (1934) converge toward zero: therefore the model of Hogate is nearly everywhere asymtotically equal to the the model of Berkhout and Plug. We also shows that the model of Berkhout et al (2004) is the asymptotic distribution of the model of Holgate (1934).…”

Section: Introductionmentioning

confidence: 60%

“…We also shows that the model of Berkhout et al (2004) is the asymptotic distribution of the model of Holgate (1934). Some graphs will be presented at the end of this paper to illustrate the comparison of these two models.…”

Section: Introductionmentioning

confidence: 94%

“…But, outside of the difficult matrix manipulations that it requires to estimate the parameters, the model of Holgate puts in evidence a strictly positive correlation. To remedy this problem, Berkhout et al (2004) proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive. Otherwise, in their paper, Berkhout and Plug reviewed the model of Holgate without comparing it to their model.…”

Section: Introductionmentioning

confidence: 99%

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Comparison between two bivariate Poisson distributions through the phi-divergence

Nganga¹,

Bidounga²,

Mizère³

et al. 2017

jas

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Abstract. In the literature, there are two probabilistic models of bivariate Poisson : the model according to Holgate and the model according to Berkhout and Plug. These two models express themselves by their probability mass function. The model of Holgate puts in evidence a strictly positive correlation, which is not always realistic. To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive. In this paper, we show that these models are nearly everywhere asymptotically equal. From this survey that the φ-divergence converges toward zero, both models are therefore nearly everywhere equal. Also, the model of Holgate converges toward the one of Berkhout and Plug. Some graphs will be presented for illustrating this comparison.

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison between two bivariate Poisson distributions through the phi-divergence

Nganga¹,

Bidounga²,

Mizère³

et al. 2017

jas

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show abstract

“…where There are some other models that allow for negative correlation (see van Ophem 1999, Chib and Winkelmann 2001, Berkhout and Plug 2004, Karlis and Melogkotsidou (2007, Nikoloulopoulos and Karlis, 2009), but they are much more complicated and require a special effort for parameter estimation. In the context of automobile insurance, it is not necessary to consider negative correlation for these type of claims.…”

Section: A Model With Common Covariancementioning

confidence: 99%

Bayesian multivariate Poisson models for insurance ratemaking

Bermúdez

Karlis

2011

Insurance: Mathematics and Economics

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When actuaries face 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 resolve this problem (and also allows us to 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 together with their zero-inflated versions.

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“…There are some other models that allow for negative correlation (see van Ophem 1999, Chib and Winkelmann 2001, Berkhout and Plug 2004, Karlis and Melogkotsidou (2007, Nikoloulopoulos and Karlis, 2009), but they are much more complicated and require a special effort for parameter estimation. In the context of automobile insurance, it is not necessary to consider negative correlation for these type of claims.…”

mentioning

confidence: 99%

Modelling Dependence in a Ratemaking Procedure with Multivariate Poisson Regression Models

Bermúdez

Karlis

2010

SSRN Journal

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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

A bivariate Poisson count data model using conditional probabilities

Cited by 64 publications

References 13 publications

Comparison between two bivariate Poisson distributions through the phi-divergence

Comparison between two bivariate Poisson distributions through the phi-divergence

Bayesian multivariate Poisson models for insurance ratemaking

Modelling Dependence in a Ratemaking Procedure with Multivariate Poisson Regression Models

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