Showing papers on "Multivariate gamma function published in 1991"
1 Jan 1991
TL;DR: In this paper, the concept of density weighting function (d.w.f) is reexamined and a new constructive approach to the generation of dependence between random variables based on this concept is proposed.
Abstract: In this paper the concept of density weighting function (d.w.f.) [6] is reexamined and a new constructive approach to the generation of dependence between random variables based on this concept is proposed. A number of well known classical distributions (including the generalized Farlie-Gumbel-Morgenstern distribution) are reinterpreted and new reparametrizations are introduced. Limits of dependence explained by d.w.f.s are examined. An elementary Lemma (stated here for the case n = 2) which serves as a key for a number of far reaching generalizations can be formulated as follows:
Let h(x,y) be a p.d.f. on the square [0, l]2, symmetric about the line y = x. If the isoprobability contours of h are of the form x-y = k(k ∈ [-1, 1]), and h(x, y) is a strictly monotone function of ∣x-y∣, then marginal densities cannot be uniform.
31 citations
TL;DR: In this paper, a new representation for the characteristic function of the joint distribution of the Mahalanobis distances betweenk independent N(μ, Σ)-distributed points is given.
Abstract: A new representation for the characteristic function of the joint distribution of the Mahalanobis distances betweenk independentN(μ, Σ)-distributed points is given. Especially fork=3 the corresponding distribution function is obtained as a special case of multivariate gamma distributions whose accompanying normal distribution has a positive semidefinite correlation matrix with correlationsϱ
ij=−a
i
a
j. These gamma distribution functions are given here by one-dimensional parameter integrals. With some further trivariate gamma distributions third order Bonferroni inequalities are derived for the upper tails of the distribution function of the multivariate range ofk independentN(μ, I)-distributed points. From these inequalities very accurate (conservative) approximations to upperα-level bounds can also be computed for studentized multivariate ranges.
18 citations
TL;DR: In this paper, the authors derive monotonicity properties of generalized entropy functionals of various multivariate distributions, including the distributions of random eigenvalues arising in many hypothesis testing problems in multivariate analysis.
3 citations
TL;DR: In this article, the lower dimensional marginal density functions of a truncated multivariate density function are derived and shown to be a function of untruncated marginal density function, appropriately defined conditional distribution function and size of the multivariate truncation region.
Abstract: The lower dimensional marginal density functions of a truncated multivariate density function is derived in general, and shown that it is a function of untruncated marginal density function, appropriately defined conditional distribution function and size of the multivariate truncation region. As a special case, lower dimensional marginal density function of a truncated multivariate normal distribution is given.
1 citations
TL;DR: In this paper, a new form of multivariate gamma is defined whose components are positively correlated and have a three parameter gamma distribution, and explicit forms of moments, moment generating function, conditional moments, and density representations are derived.