INFERENCE FOR THE QUANTILE RATIO INEQUALITY INDEX IN THE CONTEXT OF SURVEY DATA

There exist many statistical indicators for measuring economic inequality. Most of them rely on distribution moments or focus on a few selected percentiles at the tails of the distribution. Recently, a so-called quantile ratio index has been introduced. It considers the entire distribution and measures the distance between the (economic) equi-distribution scenario and the average ratio of quantiles below the median to their symmetric counterparts above it. We present a finite population framework for estimating this index and its standard error under some complex sampling designs. Our estimator demonstrates high accuracy and precision, even with relatively small samples. Being solely based on quantiles, this index exhibits remarkable robustness, having limited sensitivity to anomalous values and highly skewed distributions. This is also shown by an analysis of its influence function.