Multivariate Generalization of the Gauss Hypergeometric Distribution
نویسندگان
چکیده
The Gauss hypergeometric distribution with the density proportional to xα−1 (1− x)β−1 (1 + ξx)−γ , 0 < x < 1 arises in connection with the priori distribution of the parameter ρ (0 < ρ < 1) representing traffic intensity in a M/M/1 queue system. In this article, we define and study a multivariate generalization of this distribution and derive some of its properties like marginal densities, joint moments, and factorizations. A data application is given.
منابع مشابه
Matrix-variate Gauss Hypergeometric Distribution
In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric f...
متن کاملA generalization of Clausen’s identity
Abstract The paper aims to generalize Clausen’s identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen’s identity. The general contiguous variation of Clausen’s identity is found. The related Chaundy’s identit...
متن کاملMultivariate Generalization of the Confluent Hypergeometric Function Kind 1 Distribution
The confluent hypergeometric function kind 1 distribution with the probability density function pdf proportional to x −11F1 α; β;−x , x > 0 occurs as the distribution of the ratio of independent gamma and beta variables. In this article, a multivariate generalization of this distribution is defined and derived. Several pertinent properties of this multivariate distribution are discussed that sh...
متن کاملON AN EXTENSION OF A QUADRATIC TRANSFORMATION FORMULA DUE TO GAUSS
The aim of this research note is to prove the following new transformation formula begin{equation*} (1-x)^{-2a},_{3}F_{2}left[begin{array}{ccccc} a, & a+frac{1}{2}, & d+1 & & \ & & & ; & -frac{4x}{(1-x)^{2}} \ & c+1, & d & & end{array}right] \ =,_{4}F_{3}left[begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \ & & & & ; & -x \ & c+1, & a-A, & a+A & & end{array} right], end{equation*} wher...
متن کاملInequalities for sections of exponential function series and proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions
In the preprint [1] one of the authors formulated some conjectures on monotonicity of ratios for exponential series sections. They lead to more general conjecture on monotonicity of ratios of Kummer hypergeometric functions and was not proved from 1993. In this paper we prove some conjectures from [1] for Kummer hypergeometric functions and its further generalizations for Gauss and generalized ...
متن کامل