Sufficient conditions for negative association of random variables (Q1807837)

Negative association has been recognized as an interesting property, especially for reliability applications. The paper investigates sufficient conditions for a random vector \[ \mathbf X=(X_1,X_2,\dots,X_n) \] to be negatively associated, conditional on an increasing function, say \(\psi\). Till now, two forms of the function \(\psi\) were known to possess this property. The sum and the permutation of the randorn vector \({\mathbf X}\). The authors derive sufficient conditions that generalize the existing results for negative association. It is shown that conditional distributions based on order statistics can provide the sufficient conditions needed. The connection with the notion of negative dependence is also shown. An illustration, for a reliability scheme with a lot of components with negative association, is also given.