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March, 1977 Schur Functions in Statistics II. Stochastic Majorization
S. E. Nevius, F. Proschan, J. Sethuraman
Ann. Statist. 5(2): 263-273 (March, 1977). DOI: 10.1214/aos/1176343793


This is Part II of a two-part paper. The main purpose of this two-part paper is (a) to develop new concepts and techniques in the theory of majorization and Schur functions, and (b) to obtain fruitful applications in probability and statistics. In Part II we introduce a stochastic version of majorization, develop its properties, and obtain multivariate applications of both the preservation theorem of Part I and the new notion of stochastic majorization. This leads to a definition of Schur families of multivariate distributions. Generalizations are obtained of earlier results of Olkin and of Wong and Yue; in addition, new results are obtained for the multinomial, multivariate negative binomial, multivariate hypergeometric, Dirichlet, negative multivariate hypergeometric, and multivariate logarithmic series distributions.


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S. E. Nevius. F. Proschan. J. Sethuraman. "Schur Functions in Statistics II. Stochastic Majorization." Ann. Statist. 5 (2) 263 - 273, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0383.62039
MathSciNet: MR443225
Digital Object Identifier: 10.1214/aos/1176343793

Primary: 26A51‎
Secondary: 26A86 , 60E05 , 62H99

Keywords: Inequalities‎ , majorization , Multivariate distributions , Schur function , Schur-concave , Schur-convex , stochastic majorization

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 2 • March, 1977
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