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Monotonicity of certain multivariate normal probabilities
Author(s) -
Eaton Morris L.,
Perlman Michael D.
Publication year - 1975
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 - 10.2307/3315277
Subject(s) - monotonic function , mathematics , multivariate normal distribution , zero (linguistics) , combinatorics , multivariate statistics , regular polygon , function (biology) , distribution (mathematics) , convex function , mathematical analysis , pure mathematics , statistics , geometry , linguistics , philosophy , evolutionary biology , biology
Let (X, Y) have a (p+q)‐dimensional normal distribution and let C, K be convex symmetric sets of dimensions p, q respectively. Under certain restrictions on the mean vector it is shown that P(X ε C, Y ε K) is a monotonically increasing function of the first canonical correlation coefficient between X and Y, provided the remaining coefficients are zero.