Monotonicity of certain multivariate normal probabilities | Zendy

Eaton Morris L. | Zendy; Perlman Michael D. | Zendy

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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.

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