Departure-based Asymptotic Stochastic Order for Random Processes

TL;DR

This paper introduces a new asymptotic stochastic order for random processes using a departure measure, enabling comparison of complex data structures like mixtures of order statistics and record values in large samples.

Contribution

It proposes a novel asymptotic stochastic order based on departure measures, extending stochastic comparison methods to large-sample random processes.

Findings

Established the asymptotic stochastic order for random processes.

Applied the order to compare mixtures of order statistics.

Analyzed record values from different homogeneous samples.

Abstract

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values coming from two different homogeneous samples, as the sample size becomes large.