Related papers: A fractional generalization of the Dirichlet distr…
The Schl\"omilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with…
In this article, we study the distribution of values of Dirichlet $L$-functions, the distribution of values of the random models for Dirichlet $L$-functions, and the discrepancy between these two kinds of distributions. For each question,…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
We know that the marginals in a Dirichlet distribution are beta variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
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…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
There exist several endeavors proposing a new family of extended distributions using the beta-generating technique. This is a well-known mechanism in developing flexible distributions, by embedding the cumulative distribution function (cdf)…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha, \beta}(\lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that…
The geometry of unit $N$-dimensional $\ell_{p}$ balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest,…