The Multivariate Normal Distribution |
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a₁ a₂ applications arbitrary but fixed b₁ b₂ bivariate normal distribution c₁ c₂ canonical correlation common correlation coefficient common mean common variance o² conditional distribution convex convex set defined degrees of freedom denote density function f(x distribution function exchangeable normal variables exchangeable random variables Fact function of X1 given X₂ holds identically distributed independent inequalities joint density function k₁ Let X1 log-concave M-matrix marginal density marginal distribution Marshall and Olkin mean vector mean µ MTP2 multiple correlation multiple correlation coefficient multivariate normal distribution n-dimensional random variable nondecreasing function nonnegative nonsingular normal density function obtained order statistics P₁ P₂ permutation permutation-symmetric positive definite positive dependence probability content Probability Integral Proposition Proschan real numbers result right-hand side sample covariance matrix Schur-concave function Show symmetric t₁ tion Tong U₁ univariate V₁ values variables with means Verify X₁ Y₁ Y₂ Z₁ μ₁ σ²