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...

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...

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...

A goodness of fit test for the Pareto distribution, when the observations are subjected to Type II right censoring is proposed. The test statistic involves transformations of the original data and is based on the nonparametric Nelson-Aalen estimator of the cumulative hazard function. By Monte...

Lorenz order relationships among order statistics from exponential samples of possible different sizes are obtained.

A new stationary process with logistic marginals is described. The construction involves dependent geometric minima of independent logistic random variables. Closely related Pareto and exponential processes are introduced.