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Uniform stochastic ordering and related inequalities
Author(s) -
Keilson Julian,
Sumita Ushio
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3556181
Subject(s) - univariate , mathematics , inequality , order (exchange) , simple (philosophy) , interval (graph theory) , stochastic ordering , stochastic process , variety (cybernetics) , multivariate statistics , combinatorics , statistics , mathematical analysis , economics , finance , epistemology , philosophy
Stochastic order between univariate random variates may be called uniform when such order persists under conditioning to a broad family of intervals. The ordering is local when it holds for any finite interval ( a, b ), however small. Local order in multivariate settings has been described by Whitt (1980, 1981), by Karlin and Rinott (1980), and by others. The prevalence of uniform and local order in a variety of simple stochastic‐process settings is displayed, and inequalities arising from such orderings developed.