Negative aging and stochastic comparisons of residual lifetimes in multivariate frailty models

Abstract

Abstract Consider two random vectors X 1 and X 2 whose distributions are defined according to the multivariate frailty approach, and let X k , t = [ X k − t | X k > t ] , k = 1 , 2 , be the corresponding vectors of residual lifetimes at t = ( t 1 , … , t n ) , t i ∈ R , i = 1 , … , n . Conditions for multivariate stochastic comparisons of random vectors described by the frailty approach have been recently presented in Misra et al. (2009) . Here we prosecute their study, providing sufficient conditions for the stochastic comparison X 1 , t ≤ st X 2 , t , where t is an arbitrary vector in R n . Sufficient conditions for the stochastic comparisons X i , t ≤ st X i , t + v , where t is as above and v is a vector with non-negative components, are presented too.