Stochastic comparison of residual lifetime mixture models

In this paper, we consider stochastic comparisons of mixtures (F∗ and G∗) of residual life distributions (Fθ and Gθ, θ>0) arising out of different baseline distributions (F and G) and different mixing distributions (H1 and H2). Under certain conditions on F, G, H1 and H2, we establish that the distributions F∗ and G∗ are stochastically ordered. Further, we make stochastic comparison of mixture distribution F∗ with the distribution of residual lifetime at random time Θ1.