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Negatively superadditive dependence of random variables with applications. (English) Zbl 1050.60502
Summary: A random vector $$X=(X_1,X_2,\dots,X_m)$$ is said to be negatively superadditive dependent (NSD) if, for every superadditive function $$\varphi, E\varphi(X_1,X_2,\dots,X_m)\leq E\varphi(Y_1,Y_2,\dots,Y_m)$$, where $$Y_1,Y_2,\dots,Y_m$$ are independent with $$Y_i\overset {d}=X_i$$ for each $$i$$. Some basic properties and three structure theorems for NSD vectors are derived and applied to show that a number of well-known multivariate distributions possess the NSD property. Applications are also presented.

##### MSC:
 60E05 Probability distributions: general theory 62H20 Measures of association (correlation, canonical correlation, etc.)