Y. L. Tong

Optimal Arrangement of Components Via Pairwise Rearrangements.

Abstract : The authors introduce the notion of comparison of the criticality of two nodes in a coherent system, and develop a monotonicity property of the reliability function under component pairwise rearrangement. They use this property to find the optimal component arrangement. Worked examples illustrate the methods proposed. Keywords: Optimization; Permutations; Nodes.

Positive Dependence of a Class of Multivariate Exponential Distributions

The positive dependence of a subclass of multivariate exponential distributions is examined. This class is characterized by an index vector k and a parameter vector

A stochastic ordering of partial sums of independent random variables and of some random processes

\lambda

Crossing Properties of Mixture Distributions

, which are used as an ordering to yield degrees of positive dependence. The results presented have a direct implication on the reliability function of a system and the survival probability function of a shock model, and consequently on the optimal assembly of systems.

The Scientific Contributions Of Milton Sobel

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

Convex functions, partial orderings, and statistical applications

Mixture distributions are a frequently used tool in modelling random phenomena. We consider mixtures of densities from a one-parameter exponenvial family of distributions. Using the tools of totally positive functions and the variation-diminishing property of such, we study the effect of sign-crossing properties of two mixing densities μ 1 and μ 2 on the resulting mixture distributions f 1 and f 2 . The results enable us to make stochastic and variability cornparisons for binomial-beta, mixed Weibull, and mixed gamma distributions.

Modelling dependence in simple and indirect majority systems

This article describes the scientific contributions of Milton Sobel. It motivates his research by considering his family background, his war experiences, and his mentors and fellow students at Columbia University. His research in sequential analysis, selection, ranking, group testing, and probabilistic combinatorics are highlighted.