Positive dependence orderings
The authors introduce a positive dependence ordering called \(TP_ 2PDO\) and establish a list of nine properties of this ordering. While the \(TP_ 2\)-ordering of \textit{S. Karlin} and \textit{Y. Rinott} [see J. Multivariate Anal. 10, 467-498 (1980; Zbl 0469.60006)] is defined (in the case of densities) by \(f(x_ 1,y_ 1)g(x_ 2,y_ 2)\geq f(x_ 1,y_ 2)g(x_ 2,y_ 1)\) for \(x_ 1\leq x_ 2\), \(y_ 1\leq y_ 2\) the new ordering implies the more complicated relation \[ f(x_ 1,y_ 1)f(x_ 2,y_ 2)g(x_ 1,y_ 2)g(x_ 2,y_ 1)\leq g(x_ 1,y_ 1)g(x_ 2,y_ 2)f(x_ 1,y_ 2)f(x_ 2,y_ 1). \] The converse relation remains open.
scientific article; zbMATH DE number 4001173
scientific article