Interval estimators for ratios of independent quantiles and interquantile ranges

TL;DR

This paper develops and evaluates interval estimators for ratios of independent quantiles and interquantile ranges, demonstrating their effectiveness in accurately comparing location and scale across various distributions.

Contribution

It introduces new interval estimators for ratios of quantiles and interquantile ranges with strong coverage properties, especially useful for skewed distributions.

Findings

Intervals have excellent coverage for diverse distributions

Simulations confirm robustness for skewed data

Examples illustrate practical application in comparing location and scale

Abstract

Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of independent quantiles and interquantile ranges that will be useful when comparing location and scale for two samples. Simulations show that the intervals have excellent coverage properties for a wide range of distributions, including those that are heavily skewed. Examples are also considered that highlight the usefulness of using these approaches to compare location and scale.