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November, 1976 The Multivariate Inclusion-Exclusion Formula and Order Statistics from Dependent Variates
Willi Maurer, Barry H. Margolin
Ann. Statist. 4(6): 1190-1199 (November, 1976). DOI: 10.1214/aos/1176343650

Abstract

A variant of the general multivariate inclusion-exclusion formula of Meyer (1969) is derived for the case where $K$ classes of events are considered and specific subsets of the events, one from each class, are related to one another by set inclusion. This result, in turn, yields a formula for the cumulative distribution function of any subset of order statistics from dependent random variables in terms of cumulative distribution functions of subsets of the unordered variables. An important example of dependent random variables, where the variables are jointly distributed as a Dirichlet $D_n(1, 1, \cdots, 1)$, is discussed in detail; various authors' results for this distribution are extended, or rederived as special cases via the formulae presented.

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Willi Maurer. Barry H. Margolin. "The Multivariate Inclusion-Exclusion Formula and Order Statistics from Dependent Variates." Ann. Statist. 4 (6) 1190 - 1199, November, 1976. https://doi.org/10.1214/aos/1176343650

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0351.62034
MathSciNet: MR426287
Digital Object Identifier: 10.1214/aos/1176343650

Subjects:
Primary: 62G30
Secondary: 60C05

Keywords: Dependent random variables , Dirichlet distribution , Exchangeable random variables , Multivariate inclusion-exclusion , order statistics

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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