Showing papers on "Multivariate gamma function published in 2014"
29 Sep 2014
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
Abstract: In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics.
Keywords:
generating function;
moments;
conditional distribution;
truncated distribution;
regression;
bivariate normal;
multivariate normal;
multivariate exponential;
multivariate gamma;
dirichlet;
inverted dirichlet;
liouville;
multivariate logistic;
multivariate pareto;
multivariate extreme value;
multivariate t;
wishart translated systems;
multivariate exponential families
1,176 citations
TL;DR: For a class of skew-normal matrix distributions, the density function, moment generating function and independence conditions are obtained and a new version of Cochran’s theorem is given.
33 citations
Journal Article•
TL;DR: In this article, the authors derived a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector, using this result, the expressions of the density function as well as of the characteristic function are established.
Abstract: In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density
function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from product which leads to a considerable improvement
in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix.
15 citations
TL;DR: In this paper, the eigenvalue density of the Wishart correlation matrices using supersymmetry was calculated using a supersymmetric supersmooth supersymmetrization approach, and a closed form expression for the density was derived in terms of a fourfold integral.
Abstract: Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions The doubly correlated Wishart model takes both into account We calculate the eigenvalue density of the Wishart correlation matrices using supersymmetry In the complex case we obtain a new closed form expression which we compare to previous results in the literature In the more relevant and much more complicated real case we derive an expression for the density in terms of a fourfold integral Finally, we calculate the density in the limit of large correlation matrices
14 citations
TL;DR: In this article, a representation for a large class of n-dimensional multivariate gamma random variables as defined by Verre-Jones is given, and the probability density functions of all 2-dimensional and 3-dimensional gamma variables are given explicitly.
Abstract: A representation is given for a large class of n-dimensional multivariate gamma random variables as defined by Verre-Jones. In particular, the probability density functions of all 2-dimensional gamma random variables are given explicitly and it is shown how to obtain the probability density functions of all 3-dimensional gamma random variables.
12 citations
TL;DR: In this article, a new view on classical asymptotic expansions of the logarithm of gamma function is given, and general formulae for the expansion of the Wallis power function through polygamma functions are derived and analyzed.
Abstract: A new view on classical asymptotic expansions of the logarithm of gamma function is given. Then general formulae for the asymptotic expansions of the logarithm of gamma function and the Wallis power function through polygamma functions are derived and analysed.
5 citations
TL;DR: For a -variate density function, the point-symmetry, quasi-point symmetry of order, and marginal point symmetry were defined in this paper, and it was shown that the density function is quasi-Point-Symmetric if and only if it is pointsymmetric of order.
Abstract: For a -variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of order (), and the marginal point-symmetry of order and gives the theorem that the density function is -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of order . The theorem is illustrated for the multivariate normal density function.
2 citations
TL;DR: A derivation of real and complex anti-Wishart distribution is introduced, which can be summarized as integration of Dirac delta function in sample space with ‘Bartlett coordinate setting’.
2 citations
1 Jun 2014
TL;DR: In this article, a multivariate gamma distribution based on a linear relationship of a structural equation modeling is proposed, and the dependence in the structure is maintained, using the familiar expectation-maximization technique.
Abstract: There is an increased interest in the multivariate gamma distribution, not only in its properties and functionality but also in its parameter estimations In this work, we present a review of the multivariate gamma distribution, and propose a multivariate gamma distribution based on a linear relationship of a structural equation modeling The objective is to include proportional occurrence in the density formulation for limited data applications The dependence in the structure is maintained, and our approach uses the familiar expectation-maximization technique
1 citations
TL;DR: In this paper, the authors derived exact and compact expressions for the joint probability density and marginal density of eigenvalues for the complex Wishart case when one of the covariance matrices is proportional to the identity matrix, while the other is arbitrary.
Abstract: The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However, analytical results concerning the corresponding eigenvalue statistics have remained unavailable, even for the sum of two Wishart matrices. This can be attributed to the complicated and rotationally noninvariant nature of the matrix distribution that makes extracting the information about eigenvalues a nontrivial task. Using a generalization of the Harish-Chandra-Itzykson-Zuber integral, we find exact solution to this problem for the complex Wishart case when one of the covariance matrices is proportional to the identity matrix, while the other is arbitrary. We derive exact and compact expressions for the joint probability density and marginal density of eigenvalues. The analytical results are compared with numerical simulations and we find perfect agreement.
TL;DR: In this paper, a bivariate distribution whose marginal are gamma and beta prime distributions is introduced and the distribution is derived and the generation of such bivariate sample is shown, and extension of the results are given in the multivariate case under a joint independent component analysis method.
Abstract: A bivariate distribution whose marginal are gamma and beta prime distribution is introduced. The distribution is derived and the generation of such bivariate sample is shown. Extension of the results are given in the multivariate case under a joint independent component analysis method. Simulated applications are given and they show consistency of our approach. Estimation procedures for the bivariate case are provided.