Consider two non-negative integer-valued r.v.'s X,Y with X=Y. Suppose that the conditional distribution of Y|X is binomial with parameters (n,p), n=0,1,2,.; 0 < p < 1 and p independent of n. It is known, and can be checked easily, that under the above assumption the distribution of Y is Poisson with parameter λp, λ>0 (Poisson(λp)) if and only if (iff) X is Poisson (λ). This model has been extensively used in the literature under different names in...</p>

Compound Poisson distributions (CPD's) are frequently used as alternatives in studying situations where a simple Poisson model is found inadequate to describe. In this paper an attempt is made to identify compound Poisson distributions when it is known that the conditional distribution of two...

The binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications. The present paper examines some generalizations of these distributions with many practical applications. Properties of these generalizations are studied and models...

With the notion of success in a series of trials extended to refer to a run of like outcomes, several new distributions are obtained as the result of sampling from an urn without replacement or with additional replacements. In this context, the hypergeometric, negative hypergeometric,...

The stuttering generalized Waring distribution is introduced and shown to arise through two urn genesis schemes. Its probability generating function and moments are derived and some potential applications are discussed

In this paper, distributions of items sampled inversely in clusters are derived. In particular, negative binomial type of distributions are obtained and their properties are studied. A logarithmic series, type of distribution is also defined as limiting form of the obtained generalized negative...

The paper discusses extensions of the well-known hypergeometric and negative hypergeometric distributions for describing data with multiple counts. The derivation of these extensions is based on certain urn schemes that allow for sampling clusters of items rather than individual items. The...

A stock replenishing model is considered whereby not only the demand for the item, but also the stock in hand and the lead time period are considered to be random variables. The interrelations of these three item characteristics are then studied in the framework of a scheme for deciding when to...

The paper deals with a distribution that arises as the distribution of a sample statistic used to compare the predictive ability of two competing linear models. It is defined as the distribution of the ratio of two correlated gamma variables and its probabilities are tabulated in order that they...

The paper considers the problem of selecting one of two not necessarily nested competing regression models based on comparative evaluations of their abilities in each of two different issues: The first pertains to viewing the problem as a “best-fitting” model determination problem in the...