In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums. The PF2 property reveals the monotonicity property of the reversed failure rates of certain compound...

Poisson regression has been widely used to model count data. However, it is often criticized for its restrictive assumption of equi-dispersion, meaning equality between the variance and the mean. In real-life applications, count data often exhibits over-dispersion and excess zeroes. While Negative binomial regression is able to model count data with over-dispersion, both Hurdle (Mullahy, 1986) ...

We consider nested sequences of hierarchical loglinear models when expected frequencies are subject to linear constraints and we study the problem of finding the model in the the nested sequence that is able to explain more clearly the given data. It will be necessary to give a method to estimate the parameters of the loglinear models and also a procedure to choose the best model among the mode...

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable W satisfies a certain negative dependence assumption, then W is smaller (in the convex sense) than a Poisson variable of equal mean. Such W include those which may be written as a sum of totally negatively dependent indicators. This is generalised to other stochastic orderings. Application...

In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical da...

aim : the aim of this study was to compare alternatives methods for analysis of zero inflated count data and compare them with simple count models that are used by researchers frequently for such zero inflated data. background : analysis of viral load and risk factors could predict likelihood of achieving sustain virological response (svr). this information is useful to protect a person from ac...

We propose a novel distribution that generalizes the Multinomial distribution to enable dependencies between dimensions. Our novel distribution is based on the parametric form of the Poisson MRF model [1] but is fundamentally different because of the domain restriction to a fixed-length vector like in a Multinomial where the number of trials is fixed or known. Thus, we propose the Fixed-Length ...