Basic Definitions • Algebra of Matrices • Systems of Equations (2008)
William F. Ames, George Cain, Y. L. Tong, W. G. Steele, H. W. Coleman, R. L. Kautz, ...
Ed.
Olkin,I., Sobel,M., Tong,Y. L.
The usual formulation of the problem of selecting the best of k populations has been studied from the point of view of designing an experiment that will guarantee a certain probability of making a...
Moment and Geometric Probability Inequalities Arising from Arrangement Increasing Functions. (2002)
Boland,Philip J., Proschan,Frank, Tong,Y. L.
A real valued function g of two vector arguments x and y epsilon R sub n is said to be arrangement increasing if it increases in value as the arrangement of components in x becomes increasingly...
Convexity of Elliptically Contoured Distributions with Applications. (2002)
The problem of evaluating multivariate probabilities arises in many areas of statistics, such as in the construction of confidence regions for the mean vector or regression parameters in a general...
Inequalities for Propability Contents of Convex Sets via Geometric Average. (2002)
This paper derives such an inequality for a large class of density functions and a large class fo convex sets. The most general results are given for the bivariate case. An extention to the...
Optimal Arrangement of Components Via Pairwise Rearrangements. (1998)
Boland, Philip J., Proschan, Frank, Tong, Y. L.
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...
Some Majorization Inequalities for Functions of Exchangeable Random Variables. (1998)
Boland, Philip J., Proschan, Frank, Tong, Y. L.
This paper contains inequalities for the exceptions of permutation-invariant concave functions of the partial sums of nonnegative exchangeable random variables. Two majorization inequalities are...
Relationship between stochastic inequalities and some classical mathematical inequalities (1997)
The notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this...
Relationship between stochastic inequalities and some classical mathematical inequalities (1997)
The notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this...
On the behaviour of the probability function for selecting the best normal population (1979)
TONG, Y. L., WETZELL, DAVID E.
When selecting the best normal population with the largest mean, how does the probability function of correct selection behave when the number of observations from a given population...
Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums
Shaked, M., Shanthikumar, J. G., Tong, Y. L.
Studying the joint distributional properties of partial sums of independent random variables, we obtain stochastic analogues of some simple deterministic results from the theory of majorization,...
Inequalities for probability contents of convex sets via geometric average
It is shown that: If (X1, X2) is a permutation invariant central convex unimodal random vector and if A is a symmetric (about 0) permutation invariant convex set then P{(aX1, X2/a) [set membership,...
Some partial orderings of exchangeable random variables by positive dependence
Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such...
Concentration order on a metric space, with some statistical applications
A concept called concentration order of probability distributions on a metric space is introduced, then the norm stochastic order that compares real-parameter stochastic processes is introduced as a...