Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Central Multivariate Chi-Square and Gamma Distributions
64
0
0.0
(
0
)
Added by
Thomas Royen
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
Authors
Thomas Royen
Ask ChatGPT about the research
No Arabic abstract
A (p-1)-variate integral representation is given for the cumulative distribution function of the general p-variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known analytical functions is integrated over arguments from (-pi,pi). To facilitate the computation, these formulas are given more detailed for p=2 and p=3. These (p-1)-variate integrals are also derived for the diagonal of a non-central complex Wishart Matrix. Furthermore, some alternative formulas are given for the cases with an associated one-factorial (pxp)-correlation matrix R, i.e. R differs from a suitable diagonal matrix only by a matrix of rank 1, which holds in particular for all (3x3)-R with no vanishing correlation.
rate research
Read More
Three types of integral representations for the cumulative distribution functions of convolutions of non-central p-variate gamma distributions are given by integration of elementary complex functions over the p-cube Cp = (-pi,pi]x...x(-pi,pi]. In particular, the joint distribution of the diagonal elements of a generalized quadratic form XAX with n independent normally distributed column vectors in X is obtained. For a single p-variate gamma distribution function (p-1)-variate integrals over Cp-1 are derived. The integrals are numerically more favourable than integrals obtained from the Fourier or laplace inversion formula.
We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $chi^2$-divergence on signed finite measures. The asymptotic properties of the proposed estimate and the test statistic are studied under the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not.
We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial differential equations for the Fisher-Bingham distribution.
We show that the distribution of the scalar Schur complement in a noncentral Wishart matrix is a mixture of central chi-square distributions with different degrees of freedom. For the case of a rank-1 noncentrality matrix, the weights of the mixture representation arise from a noncentral beta mixture of Poisson distributions.
We discuss two research areas dealing respectively with (1) a class of multivariate medians and (2) a symmetrization algorithm for probability measures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
