For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of...

We establish the exact expression of the density of Wilks's statistic [Lambda](n,p,q), and also those of the densities of the product and ratio of two independent such statistics, in terms of Meijer functions, and provide applications with numerical illustrations in various domains of...

The term grouped data refers to the case where the exact value of the characteristic of interest is either unknown or difficult to register. In the present article we study a model that can be used for the simultaneous control of two (possibly correlated) variables whose values have been...

Let X1,...,Xn be a random sample from an absolutely continuous distribution with non-negative support, and let Y1,...,Yn be mutually independent lifetimes with proportional hazard rates. Let also X(1)...X(n) and Y(1)...Y(n) be their associated order statistics. It is shown that the pair...

Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative...

The purpose of this paper is to investigate the effect of nonnormality upon the nonnull distributions of some MANOVA test statistics under normality. It is shown that whatever the underlying distributions, the difference of the local powers up to order N-1 (N is the total number of observations)...

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often...

This paper discusses linear regression of strongly correlated data that arises, for example, in magnetohydrodynamic equilibrium reconstructions. We have proved that, generically, the covariance matrix of the estimated regression parameters for fixed sample size goes to zero as the correlations...

This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately normalized eigenvectors and eigenvalues asymptotically...

The main objective of this paper is the calculation and the comparative study of two general measures of multivariate kurtosis, namely Mardia's measure [beta]2,p and Song's measure . In this context, general formulas for the said measures are derived for the broad family of the elliptically...