A Test for “Intrinsic Correlation” in the Theory of Accident Proneness

Kocherlakota, S.

doi:10.1111/j.2517-6161.1966.tb00631.x

Cited by 32 publications

(17 citation statements)

References 5 publications

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“…Our model generalizes this idea in the sense that we start from a bivariate model while their model was based on two independent Poisson distributions. Following the terminology of Subrahmaniam (1966), our model assumes intrinsic correlation as well (measured by θ 3 ) and thus it is much more general. Our advance is that we also assume a multivariate prior allowing for correlation between the parameters but in our case the posterior can be obtained in closed form without the need of MCMC or approximations.…”

Section: Discussionmentioning

confidence: 99%

Exact Bayesian modeling for bivariate Poisson data and extensions

Karlis

Tsiamyrtzis

2007

Stat Comput

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Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics just to name a few) and the bivariate Poisson distribution being a generalization of the Poisson distribution plays an important role in modelling such data. In the present paper we present a Bayesian estimation approach for the parameters of the bivariate Poisson model and provide the posterior distributions in closed forms. It is shown that the joint posterior distributions are finite mixtures of conditionally independent gamma distributions for which their full form can be easily deduced by a recursively updating scheme. Thus, the need of applying computationally demanding MCMC schemes for Bayesian inference in such models will be removed, since direct sampling from the posterior will become available, even in cases where the posterior distribution of functions of the parameters is not available in closed form. In addition, we define a class of prior distributions that possess an interesting conjugacy property which extends the typical notion of conjugacy, in the sense that both prior and posteriors belong to the same family of finite mixture models but with different number of components. Extension to certain other models including multivariate models or models with other marginal distributions are discussed.

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Section: Discussionmentioning

confidence: 99%

Exact Bayesian modeling for bivariate Poisson data and extensions

Karlis

Tsiamyrtzis

2007

Stat Comput

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“…(i) Bivariate Negative Binomial Edwards and Gurland (1961) and Subrahmaniam (1966) have independently developed the generalized version of the Bates-Neyman model. Here ~ is taken to have the two parameter gamma distribution with pdf…”

Section: Examplesmentioning

confidence: 99%

“…This is given by: Subrahmaniam (1966) has shown that the generating function is given by In the particular cases we study below, the r.v. Y2 will be seen to be a convolution itself.…”

Section: Recurrence Relationsmentioning

confidence: 99%

“…On the other hand, several authors have examined the problem where wi= zAi, i= 1,2, 3 with 21,22, 23 being constants and r a random variable characterizing an 'individual' in the population. Such models have been considered among others by Holgate (1966), Subrahmaniam (1966), Gillings (1974) and Kemp and Papageorgiou (1982). In each case z is assumed to have a distribution of the discrete or continuous type.…”

Section: Introductionmentioning

confidence: 99%

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On the compounded bivariate Poisson distribution: A unified treatment

Kocherlakota

1988

Ann Inst Stat Math

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“…In this case, the use of bivariate negative binomial (BNB) distribution is a sound alternative. In fact, Subrahmaniam [5] and Subrahmaniam and Subrahmaniam [6] suggested a BNB distribution that is obtained from a gamma mixture of a BP distribution. Other types of BNB distributions were suggested by [7], who proposed the BNB distributions using a gamma mixture of two independent Poisson distributions, and Lee and Ong [8], who used the trivariate reduction technique from three independent negative binomial (NB) random variables.…”

Section: Introductionmentioning

confidence: 97%