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...

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...

A model of Markov dependent trials is considered that leads to a generalization of the binomial distribution in the context of evaluating models of a time series by exploiting the sequential nature of model-based predictions. Adopting an evaluation method similar in nature to that suggested by...

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...

The Yule distribution is shown to have certain interesting properties in the area of regression analysis. In particular, it is shown that under certain conditions, a random variable Z will have linear regressions on another random variable X and on its observable part Y only when X has a Yule...

The bivariate generalized Waring distribution results as a mixture of the double Poisson distribution. In this paper some probability models are considered that give rise to alternative bivariate forms of the generalized Waring distribution

Mixed Poisson distributions have been used in a wide range of scientific fields for modelling non-homogeneous populations. This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential...

This article provides two characterizations of Mardia's Type I bivariate Pareto distribution. In particular, it is shown that the distribution of a random vector (X,Y) is uniquely determined as a Mardia's Type I bivariate Pareto distribution if its weighted form follows a Mardia's Type I...