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On the sampling distributions of classical statistics in multivariate analysis

On the sampling distributions of classical statistics in multivariate analysis
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Asymptotic Distributions of Multivariate Intermediate Order Statistics

Theory of Probability & Its Applications, 1997
Summary: Let \(\{X_n= (X_n^{(1)}, \dots, X_n^{(d)})\), \(n\geq 1\}\) be independent, identically distributed random vectors with a common nondegenerate distribution function and for each \(n \geq 1\) and each \(k=1, \dots, d\), denote \(X_{1;n}^{(k)} \leq\cdots \leq X_{n;n}^{(k)}\) as the order statistics of \(X_1^{(k)}, \dots, X_n^{(k)}\).
Cheng, S (Shihong), de Haan, Laurens, Yang, J   +2 more
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Statistical inference for a class of multivariate negative binomial distributions [PDF]

, 2010
This paper considers statistical inference procedures for a class of models for positively correlated count variables called -permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been studied in the literature, while this is the first ...
Rubak, Ege H., Møller, Jesper, McCullagh, Peter   +2 more
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Concomitants of multivariate order statistics from multivariate elliptical distributions

Communications in Statistics - Theory and Methods, 2016
ABSTRACTIn this article, we consider a (k + 1)n-dimensional elliptically contoured random vector (XT1, X2T, …, XTk, ZT)T = (X11, …, X1n, …, Xk1, …, Xkn, Z1, …, Zn)T and derive the distribution of concomitant of multivariate order statistics arising from X1, X2, …, Xk.
Roohollah Roozegar, Ahad Jamalizadeh, Alireza Nematollahi   +2 more
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Descriptive statistics for multivariate distributions

Statistics & Probability Letters, 1983
Abstract The purpose of this paper is to study the concepts location, scatter, skewness and kurtosis of multivariate distributions. Measures of these properties are introduced which include some new generalizations of well-known univariate statistics. Previous work is briefly reviewed.
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Statistical Bayesian Estimation for Multivariate T-Distributions

Journal of Mathematical Sciences, 2001
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On the multivariate distributions of order statistics of discrete-state processes

[Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, 1991
The authors consider the problem of determining the multivariable joint probability distributions of the order statistics of discrete-state processes whose elements are independent and identically distributed. Two methods, the indirect and direct methods, are presented and compared in terms of their inherent computational complexity. Recursive formulae
Don M. Raymond, Moustafa M. Fahmy
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Multivariate T-Normal Distributions in Applied Statistics

Journal of Mathematical Sciences, 2001
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Statistical Distributions in Univariate and Multivariate Edgeworth Populations

Biometrika, 1976
SUMMARY A general method is presented for the formal construction of statistical distributions in univariate and multivariate populations, when the underlying distributions are specifiable by Edgeworth-type expansions. It is shown that the distribution of a statistic may be derived in principle from the appropriate normal-theory noncentral distribution,
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On the Distances Between Certain Distributions in Multivariate Statistical Analysis*

Journal of Mathematical Sciences, 2015
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