Title: Dispersion inference in small samples
Authors: Paul Kattuman - University of Cambridge (United Kingdom) [presenting]
Jun Ma - (China)
Abstract: The aim is to present a family of measures of dispersion in the general sense that encompasses inequality, concentration, heterogeneity, diversity and so on for non-negative small samples. Dispersion in a sample is measured as the probability of majorization (Lorenz dominance) relations between it and a random sample drawn from a suitable symmetric multi-variate reference distribution chosen to serve as a benchmark. One example of a reference distribution is the uniform distribution on the standard $n$ less one simplex, according to which all samples of size $n$ are equi-probable. The probabilities of majorization so defined are the $p-$values for the hypothesis that the sample of interest and a random sample from the reference distribution are of equal dispersiveness. Unlike other summary indices of dispersion, these probability measures directly enable inference, and satisfy properties desirable in any general measure of dispersion. The choice of reference distribution in this approach permits inference on the heaviness of tails.