Julio Mulero

TL;DR: An Introduction to Stochastic orders discusses the powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics as discussed by the authors.

TL;DR: This paper considers, for each component, a class of candidate models, which are obtained by combining failure rate models with imperfect maintenance models by formalizing the uncertainty on the occurrence of failures and on the effect of maintenance activities.

TL;DR: In this article, the authors considered the multivariate aging notions, defined by means of stochastic comparisons between two different pairs of residual lifetimes, at any time t, s, ≥ 0 and the case of dependent lifetimes having different distributions.

TL;DR: In this paper, sufficient conditions for multivariate stochastic comparisons of random vectors described by the multivariate frailty approach were investigated, and sufficient conditions were also provided for the stochastically comparison X 1, t ≤ st X 2, t, where t is an arbitrary vector in R n.

TL;DR: In this article, a quantile-based probabilistic mean value theorem was proposed for nonnegative random variables with nonnegative residual-lifetime distributions. But the quantile function is not a generalization of the cumulative distribution function.