A new stochastic order based on discrete Laplace transform and some ordering results of the order statistics

TL;DR

This paper introduces a novel stochastic order based on discrete Laplace transforms, exploring its properties and applications in order statistics, frailty models, and reliability, especially with random sample sizes.

Contribution

It proposes a new stochastic order using discrete Laplace transforms and derives ordering results for order statistics with applications in frailty and reliability models.

Findings

Established ordering results for order statistics under the new stochastic order.

Applied the order to frailty models and reliability analysis.

Demonstrated the usefulness of the order in practical stochastic modeling.

Abstract

This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving ordinary and fractional order statistics. Some applications in frailty models and reliability are presented as well.