A multivariate generalization of Shaked's bivariate families which are dependent by total positivity (DTP) is introduced. Some interrelationships and inequalities are generalized. Monotonicity properties of conditional hazard rate and mean residual life functions of some multivariate DTP families are investigated. Relationships with other positive dependence concepts are given.
"Dependence by Total Positivity." Ann. Probab. 13 (2) 572 - 582, May, 1985. https://doi.org/10.1214/aop/1176993010