Showing papers on "Multivariate gamma function published in 2016"
TL;DR: In this paper, the authors investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models.
Abstract: Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strate...
33 citations
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TL;DR: In this paper, a holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived.
Abstract: A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density function is derived (for m=2,3) or conjectured.
1 citations
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TL;DR: In this article, the distribution of the ratio of two central Wishart matrices with different covariance matrices is studied and its cumulative distribution function can be expressed in terms of the hypergeometric function 2F1 of a matrix argument.
Abstract: We study the distribution of the ratio of two central Wishart matrices with different covariance matrices. We first derive the density function of a particular matrix form of the ratio and show that its cumulative distribution function can be expressed in terms of the hypergeometric function 2F1 of a matrix argument. Then we apply the holonomic gradient method for numerical evaluation of the hypergeometric function. This approach enables us to compute the power function of Roy's maximum root test for testing the equality of two covariance matrices.
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TL;DR: In this paper, a set of commands that allow users to compute the distribution function, density, equi-coordinate quantiles, and random vectors of the multivariate normal and multivariate t distributions are presented.
Abstract: A set of commands that allow users to compute the distribution function, density, equi-coordinate quantiles, and random vectors of the multivariate normal and multivariate t distributions. Any non-degenerate cases of the multivariate normal and multivariate t distributions can be worked with, along with a particular class of non-central multivariate t distributions. The commands are written in a combination of Stata and Mata for speed.
1 Jan 2016
TL;DR: In this paper, the authors considered multivariate gamma distributions of third and higher dimensions and showed that these distributions are infinitely divisible in certain special cases, and extended a result of one of the authors for the corresponding bivariate distribution.
Abstract: SUMMARY. Multivariate gamma distributions of third and higher dimension are considered and shown to be infinitely divisible in certain special cases. This extends, for these special cases, a result of one of the authors for the corresponding bivariate distribution.