For a fixed [alpha] 0, the totality of bivariate densities with all conditionals being of the Pareto ([alpha]) form is identified. The resulting family is of the form F(x, y) [is proportional to] [1 + [lambda]1x + [lambda]2y + [phi][lambda]1[lambda]2xy]-([alpha]+1) for suitable choices of...

Suppose (X,Y) has a (k+1)-dimensional Cauchy distribution. Consider the conditional distribution of X given Yy0, for some fixed value of . The resulting distribution is the multivariate skewed Cauchy, in which there is truncation with respect to Y: this is but one of a general class of skewed...

Let {Yn} be a sequence of i.i.d. non-negative extended real valued random variables. For c 0, consider stationary stochastic processes of the form Xn = c min(Xn-1, Yn). Subject to a regularity condition related to the behavior of FYn(y) in a neighborhood of 0, it is verified that the associated...

This paper uses an extension of a theorem of Polya to derive bounds for the variance of a random variable. These are applied to maxima and minima of a sample and the bounds are found to be quite good.

Suppose that a system consists of n independent components and that the lifelength of the ith component is a random variable . For k[set membership, variant]{1,2,...,n-1}, denote by , the residual lifelengths of the remaining functioning components following the kth failure in the system. We...

Increasing sample size decreases the inequality of the sample mean as measured by the Lorenz order. A similar result occurs in the case of sample medians from symmetric distributions. In certain cases the sample median can be expected to be Lorenz ordered with respect to the sample mean. The...

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.

For a two-dimensional probability distribution represented as a contingency table, an algorithm due to Mosteller (1968) "standardizes" the table to have uniform marginals so as to obtain its "uniform marginals representation (UMR)". In this note, this algorithm is first shown to minimize the...

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,...

This article is concerned with parameter estimation under ranked set sampling (RSS) and under a generalized version of RSS (i.e., in the ith sample, Xri:ni is observed instead of Xi:n, so that the data are . Bayesian parameter estimation of specified parameters under both balanced and...