Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability

TL;DR

This paper establishes easy-to-verify sufficient conditions based on likelihood ratio unimodality for comparing discrete random variables using stochastic orders, with applications in reliability and parametric distribution comparison.

Contribution

It provides new sufficient conditions for stochastic orders of discrete variables, filling a gap in the literature and aiding in reliability analysis.

Findings

Conditions based on likelihood ratio unimodality are effective for stochastic order comparison.

Results simplify comparison when closed-form survival functions are unavailable.

Applications include comparing various parametric discrete distributions.

Abstract

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality of the likelihood ratio for the comparison in some stochastic orders of two discrete random variables. These results have interest in comparing discrete random variables because the sufficient conditions are easy to check when there are no closed expressions for the survival functions, which occurs in many cases. In addition, the results are applied to compare several parametric families of discrete distributions.