The random vector x is said to have an elliptical contoured distribution provided its characteristic function (c.f.) is exp([radical sign]- 1 t'[mu]) [phi] (t' [Sigma]t) for all t [epsilon] Rp, where [mu] [epsilon] Rp and [Sigma] is positive semi-definite. When [mu] = 0 and [Sigma] = I, the...

Let x have a spherical distribution (SD), with characteristic function [phi](t't), t [epsilon] Tp, to be denoted by x [approximate] Sp([phi]). Let x'Ax be a quadratic form, with A = A'. A correction is given to Theorem 1 in Khatri and Mukerjee (1987), wrongly asserting that if Q = x'Ax is...

It is established that a vector variable (X1, ..., Xk) has a multivariate normal distribution if for each Xi the regression on the rest is linear and the conditional distribution about the regression does not depend on the rest of the variables, provided the regression coefficients satisfy some...

In this paper the distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complex multivariate normal distribution is investigated. Some simplifications in the noncentral distribution are made and the noncentral distribution is derived for the special case...

Let S be distributed as noncentral Wishart given by Wp(m, [Sigma], [Omega]) and let x be an n - 1 random vector distributed as N([mu], V). If qi = x'Aix + 2l'ix + ci, i = 1, 2,..., p, are p dependent second degree polynomials in the elements of x where Aj's are symmetric matrices, then the...

Asymptotic confidence bounds on the location parameters of the linear growth curve, asymptotic distribution of the canonical correlations and asymptotic confidence bounds on the discriminatory value for the linear discriminant function are established when a set of independent observations are...

The main aim of this paper is to solve the functional equations and k 1, in vector variables t1,...,tk satisfying the condition ti = ([Sigma]j = 1m tij2)1/2 [delta] for all i, where C[alpha]i, B[alpha]j and Aij are given square matrices and d[alpha] is a given vector. The elements of the...