Keywords and Phrases: Extension of trivariate reduction Meixner class of polynomials and Srivastava's triple hypergeometric series Canonical expansions and quadrant dependence Mixed Poisson distribution Computer generation of bivariate samples Multivariate extensions and goodness-of-fit a b s t r a c t In this paper, we consider a new class of bivariate negative binomial distributions having ma...

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density described by Johnson and Kotz. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more exible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in...

This paper proposes the bivariate noncentral chi-square (BNC) distribution by compounding the Poisson probabilities with the bivariate central chi-square distribution. The probability density and cumulative distribution functions of the joint distribution of the two noncentral chi-square variables are derived for arbitrary values of the correlation coefficient, degrees of freedom(s), and noncen...

A unified treatment is presented here of compounding with the bivariate Poisson distribution. Exploiting the exponential nature of its probability generating function, it is shown that the pgf of the compound distribution is the moment generating function of the compounding random variable. This relationship leads to rather interesting general results. Particularly, the development of the condi...

We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employ...

We define the class of bivariate binomial distributions as Poisson distributions transformed by a binomial dilution and mixing with a gamma distribution. They are used to study the number of nematodes, considering the sex ratio, parasitizing birds.

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties o...

In this article we construct bivariate discrete distribution in Z. We make use of a generalized trivariate reduction technique. The special case leading to bivariate Skellam distributions is studied in detail. Properties of the derived models as well as estimation are examined. Real data application is provided. Discussion of extensions to different models is also mentioned.

Bivariate Poisson regression models for ratemaking in car insurance has been previously used. They included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. These models are now revisited in order to consider alternatives. A 2-finite mixture of bivariate Poisson regression models is used to demonstrate that the overdispersion in the data requires m...