  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.
