Related papers: The Two Ignored Components of Random Variation
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
In this paper, we present three remarkable properties of the normal distribution: first that if two independent variables's sum is normally distributed, then each random variable follows a normal distribution (which is referred to as the…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
The literature has covered the features and uses of the traditional univariate and bivariate logistic distributions in great detail. It is reasonable to wonder, though, if logistic marginals and conditionals could exhibit a similar…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…