二维正态分布矩形区域概率质量的局部单调性(英文)

Local Monotonicity of Probabilities of Rectangular Regions Under Bivariate Normal Distributions

研究了二维正态分布矩形区域概率质量当矩形区域中心沿某特定方向平移时的局部单调性。同时给出了一簇矩形区域,其中任一矩形区域的概率质量对正态分布相关系数的绝对值具有局部单调性。

Let (X_1, X_2)'～N_2(0, ∑), where ∑=and |ρ|<1, the monotonicity of the probability of a rectangular region is given when the center of the region is shifted to special directions. We also present a class of rectangular region whose probabiLity increases with absolute correlation coefficient |ρ|, 0 ≤|ρ|≤ρ_0, where 0≤ρ_0≤1 is fixed.