The shortest confidence interval for the ratio of quantiles of the Dagum distribution

Jȩdrzejczak et al. (REVSTAT-Statistical Journal 19(1), 87–97, 2021) 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 resulted in 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 calculations show a reduction in the length of the proposed confidence interval by several percent compared to the symmetrical confidence interval.