Probabilistic mean value theorems for conditioned random variables with applications.

Di Crescenzo, Antonio; Psarrakos, Georgios

In this paper, we propose a probabilistic analogue of the mean value theorem for conditional nonnegative random variables ordered in the hazard rate and reversed hazard rate order, upon conditioning on intervals of the form (t,∞) and [0,t]. This result is then specialized within the proportional hazards model and the proportional reversed hazards model with applications to series systems in reliability theory and to absorption random times of linear birth‐death processes. We also study the comparison of residual entropies and discuss some connections to Wasserstein and stop‐loss distances of random variables. A treatment for the additive hazard rate model is finally provided, with an application to life annuities.

RANDOM variables; MEAN value theorems; SYSTEMS theory; ENGINEERING reliability theory; PROPORTIONAL hazards models; RELIABILITY in engineering

Applied Stochastic Models in Business & Industry, 2019, Vol 35, Issue 4, p923

1524-1904

Academic Journal

10.1002/asmb.2427