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A chain of inequalities for some types of multivariate distributions, with nine special cases

Aplikace matematiky

Metrika

Metrika

A generalization of Wishart density for the case when the inverse of the covariance matrix is a band matrix

Mathematica Bohemica

In a multivariate normal distribution, let the inverse of the covariance matrix be a band matrix. The distribution of the sufficient statistic for the covariance matrix is derived for this case. It is a generalization of the Wishart distribution. The distribution may be used for unbiased density estimation and construction of classification rules.

A new approach to multiple class pattern classification with random matrices.

Journal of Applied Mathematics and Decision Sciences

A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms

Applicationes Mathematicae

This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).

A note on the matrix Haffian.

Qüestiió

This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X).Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

A recursion formula for expected negative and positive powers of the central Wishart distribution.

SORT

We use Haff's fundamental identity to express the expectation of Sp in lower-order terms, where S follows the central Wishart distribution.

A zero-inflated occupancy distribution: Exact results and Poisson convergence.

International Journal of Mathematics and Mathematical Sciences

Association entre variables qualitatives ordinales «nettes» ou «floues»

Statistique et analyse des données

Asymmetric semilinear copulas

Kybernetika

We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by $1/16$. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of $\Pi$ and $M$.

Asymptotic covariances for the generalized gamma distribution

Applicationes Mathematicae

The five-parameter generalized gamma distribution is one of the most flexible distributions in statistics. In this note, for the first time, we provide asymptotic covariances for the parameters using both the method of maximum likelihood and the method of moments.

Asymptotic distribution of rank statistics used for multivariate testing symmetry (Preliminary communication)

Commentationes Mathematicae Universitatis Carolinae

Asymptotic normality of multivariate linear rank statistics under general alternatives

Aplikace matematiky

Let ${X}_{j},1\le j\le N$, be independent random $p$-vectors with respective continuous cumulative distribution functions ${F}_{j}1\le j\le N$. Define the $p$-vectors ${R}_{j}$ by setting ${R}_{ij}$ equal to the rank of ${X}_{ij}$ among ${X}_{ij},...,{X}_{iN},1\le i\le p,1\le j\le N$. Let ${a}^{\left(N\right)}\left(.\right)$ denote a multivariate score function in ${R}_{p}$, and put $S={\sum }_{j=1}^{N}{c}_{j}{a}^{\left(N\right)}\left({R}_{j}\right)$, the ${c}_{j}$ being arbitrary regression constants. In this paper the asymptotic distribution of $S$ is investigated under various sets of conditions on the constants, the score functions, and the underlying distribution functions. In particular, asymptotic normality of $S$ is established...

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Applications of Mathematics

By using three theorems (Oktaba and Kieloch ) and Theorem 2.2 (Srivastava and Khatri ) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant $|{\sigma }^{2}\sum |$ in the MGM model $\left(U,XB,{\sigma }^{2}\sum \otimes V\right)$, $\sum >0$, scalar ${\sigma }^{2}>0$, with a matrix $V\ge 0$. A known $n×p$ random matrix $U$ has the expected value $E\left(U\right)=XB$, where the $n×d$ matrix $X$ is a known matrix of an experimental design, $B$ is an unknown $d×p$ matrix of parameters and ${\sigma }^{2}\sum \otimes V$ is the covariance matrix of $U,\phantom{\rule{0.166667em}{0ex}}\otimes$ being the symbol of the Kronecker...

Bayesian inference in group judgement formulation and decision making using qualitative controlled feedback.

Trabajos de Estadística e Investigación Operativa

This paper considers the problem of making statistical inferences about group judgements and group decisions using Qualitative Controlled Feedback, from the Bayesian point of view. The qualitative controlled feedback procedure was first introduced by Press (1978), for a single question of interest. The procedure in first reviewed here including the extension of the model to the multiple question case. We develop a model for responses of the panel on each stage. Many questions are treated simultaneously...

Bivariate gamma distribution as a life test model

Aplikace matematiky

The bivariate gamma distribution is taken as a life test model to analyse a series system with two dependent components $x$ and $y$. First, the distribution of a function of $x$ and $y$, that is, minimum $\left(x,y\right)$, is obtained. Next, the reliability of the component system is evaluated and tabulated for various values of the parameters. Estimates of the parameters are also obtained by using Bayesian approach. Finally, a table of the mean and variance of minimum $\left(x,y\right)$ for various values of the parameters involved is...

Metrika

Bounds for trivariate copulas with given bivariate marginals.

Journal of Inequalities and Applications [electronic only]

Central limit theorems for linear spectral statistics of large dimensional F-matrices

Annales de l'I.H.P. Probabilités et statistiques

In many applications, one needs to make statistical inference on the parameters defined by the limiting spectral distribution of an F matrix, the product of a sample covariance matrix from the independent variable array (Xjk)p×n1 and the inverse of another covariance matrix from the independent variable array (Yjk)p×n2. Here, the two variable arrays are assumed to either both real or both complex. It helps to find the asymptotic distribution of the relevant parameter estimators associated with the...

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