# The Shortest Confidence Interval for the Ratio of Quantiles of the Dagum Distribution

## TL;DR

This paper derives the shortest asymmetric confidence interval for the ratio of quantiles in the Dagum distribution, improving interval length over symmetric methods used in income distribution analysis.

## Contribution

It introduces a method to construct the shortest asymmetric confidence interval for the ratio of quantiles in the Dagum distribution, enhancing precision over existing symmetric intervals.

## Key findings

- Shortest confidence interval is asymmetric and shorter than symmetric ones.
- Interval length reduced by several percent.
- Method shown to exist and be practically obtainable.

## Abstract

J\k{e}drzejczak et al. (2018) constructed a confidence interval for a ratio of quantiles coming from the Dagum distribution, which is frequently applied as a theoretical model in numerous income distribution analyses. The proposed interval is symmetric with respect to the ratio of sample quantiles, which result may be unsatisfactory in many practical applications. The search for a confidence interval with a smaller length led to the derivation of the shortest interval with the ends being asymmetric relative to the ratio of sample quantiles. In the paper, the existence of the shortest confidence interval is shown and the method of obtaining such an interval is presented. The results of the calculation show a reduction in the length of the confidence intervals by several percent in relation to the symmetric confidence interval.