If X is a k-dimensional random vector, we denote by X(i,j) the vector X with coordinates i and j deleted. If for each i, j the conditional distribution of Xi, Xj given X(i,j) = x(i,j) is classical bivariate normal for each then it is shown that X has a classical k-variate normal distribution.

If X is a k-dimensional random vector, we denote by X(i) the vector X with coordinate i deleted and by X(i,j) the vector X with coordinates i and j deleted. If for each i the conditional distribution of Xi given X(i) = x(i) is univariate normal for each x(i) [there exists]K-1 and if for each i,...

A k-dimensional density function is determined by certain combinations of marginal and conditional densities. The present paper identifies all possible such specifications. Gelman and Speed (1993) have treated the finite discrete case of this problem. The present paper extends their work to a...

Two new concepts of order statistics for multivariate samples are introduced. In one of the versions it turns out that not every multivariate order statistic is present in every sample. These order statistics have application in multivariate ranked set sampling and can be used to generate broad...

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...