Sufficient conditions for some transform orders based on the quantile density ratio

TL;DR

This paper establishes sufficient conditions for certain transform orders involving non-monotone quantile density ratios, aiding comparison of complex or implicitly defined random variables and exploring relationships among aging concepts.

Contribution

It provides new sufficient conditions for transform orders with non-monotone quantile density ratios, extending the comparison tools for complex distributions and aging notions.

Findings

Conditions for non-monotone quantile density ratios

Comparison of Tukey generalized distributions

New relationships among aging concepts

Abstract

In this paper we focus on providing sufficient conditions for some transform orders for which the quantile densities ratio is non-monotone and, therefore, the convex transform order does not hold. These results are interesting for comparing random variables with a non-explicit expression of their quantile functions or they are computationally complex. In addition, the main results are applied to compare two Tukey generalized distributed random variables and to establish new relationships among non-monotone and positive aging notions.