  Many measures of peakedness, heavy-tailedness and kurtosis have been proposed
in the literature, mainly because kurtosis, as originally defined, is a complex
combination of the other two concepts. Insight into all three concepts can be
gained by studying Ruppert's ratios of interquantile ranges. They are not only
monotone in Horn's measure of peakedness when applied to the central portion of
the population, but also monotone in the practical tail-index of Morgenthaler
and Tukey, when applied to the tails. Distribution-free confidence intervals
are found for Ruppert's ratios, and sample sizes required to obtain such
intervals for a pre-specified relative width and level are provided. In
addition, the empirical power of distribution-free tests for peakedness and
bimodality are found for symmetric beta families and mixtures of $t$
distributions. An R script that computes the confidence intervals is provided
in online supplementary material.
