Ordering and selecting extreme populations by means of entropies and divergences

This paper studies the simultaneous selection of extreme populations from a set of independent populations. Two types of subset selection rules for k populations are proposed and studied. The first type selects one subset of populations that should contain the population with the smallest, and another subset of populations that should contain the population with the largest, φ-entropy. The second type selects analogously, but in terms of the extreme ?-divergences with respect a known control population. Properties of the proposed procedures are stated and studied. Examples are presented in order to illustrate the results.