Showing papers on "Multivariate gamma function published in 2007"
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TL;DR: In this article, a multivariate probability model possessing a dependence structure that is reflected in its variance covariance structure and gamma distributed univariate margins is introduced and studied, in particular, the higher order moments and cumulants, Chebyshev type inequalities and multiivariate probability distribution functions are derived.
Abstract: A multivariate probability model possessing a dependence structure that is reflected in its variance covariance structure and gamma distributed univariate margins is introduced and studied. In particular, the higher order moments and cumulants, Chebyshev’s type inequalities and multivariate probability distribution functions are derived. The herein suggested model is believed to be capable of describing dependent insurance losses.
64 citations
TL;DR: In this article, a generalized location scale family of multivariate gamma distributions with three-parameter gamma marginals has been proposed, which is not necessarily restricted to those with gamma marginal distributions.
Abstract: SYNOPTIC ABSTRACTIn this paper, we proffer a new multivariate gamma distribution with potential applications in survival and reliability modeling. The multivariate distribution is not necessarily restricted to those with gamma marginal distributions. We provide and characterize a generalized location scale family of multivariate gamma distributions. This family possesses three-parameter gamma marginals (in most cases) and it contains absolutely continuous classes, as well as, the Marshall Olkin type of distributions with a positive probability mass on a set of measure zero. Maximum likelihood estimators are developed in the bivariate case.
11 citations
TL;DR: This paper develops the influence analysis for the data from multivariate t distributions based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm and treats the weights as the missing data.
Abstract: For the data from multivariate t distributions, it is very hard to make an influence analysis based on the probability density function since its expression is intractable. In this paper, we present a technique for influence analysis based on the mixture distribution and EM algorithm. In fact, the multivariate t distribution can be considered as a particular Gaussian mixture by introducing the weights from the Gamma distribution. We treat the weights as the missing data and develop the influence analysis for the data from multivariate t distributions based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. Several case-deletion measures are proposed for detecting influential observations from multivariate t distributions. Two numerical examples are given to illustrate our methodology.
9 citations
TL;DR: In this paper, a generalization of the classical random sampling scheme is suggested, based on the proposed generalization one can derive many new minimum variance unbiased estimators for probabilities, as well as for other functions of unknown parameters.
Abstract: A generalization of the classical random sampling scheme is suggested. Based on the proposed generalization one can derive many new minimum variance unbiased estimators for probabilities, as well as for other functions of unknown parameters, for the multivariate Polya, the multivariate negative Polya, the multinomial, the multivariate hypergeometric, the multivariate Poisson, and the Wishart probability distributions.
2 citations
TL;DR: In this paper, the authors studied the risk dominance problem of the restricted maximum likelihood estimators of mean matrices with respect to the Kullback-Leibler loss function over restricted parameter space under the simple tree ordering set.
2 citations
TL;DR: The notion of pseudo-inverse multivariate/matrix-variate distributions was introduced in this article. But the distribution of the Moore-Penrose inverse of a random matrix is not known.
TL;DR: In this paper, simple, exact and computationally efficient expressions for the cumulative distribution function and the probability density function of the lth largest eigenvalue of a Wishart matrix are presented.
Abstract: Simple, exact and computationally efficient expressions for the cumulative distribution function and the probability density function of the lth largest eigenvalue of a Wishart matrix are presented. The results are important in the performance analysis of multiple-input, multiple-output systems operating over Rayleigh fading channels.
TL;DR: In this paper, the moments of traces of monomials in independent complex Wishart matrices were derived for the cumulants and the multivariate normal approximation to the traces of finite families of polynomials.
Abstract: We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the cumulants. From the latter, we read out the multivariate normal approximation to the traces of finite families of polynomials in independent complex Wishart matrices.