Quantiles of Sums and Expected Values of Ordered Sums.

摘要

Watson & Gordon (1986) investigated the relationship between the quantiles of a sum of independent continuous random variables and the sum of the individual quantiles. In this note some further results are obtained. Also corresponding relationships are developed for the expected values of the order statistics of a sum, and for the sum of the expected values of the individual order statistics. Keywords: Inequalities; Order statistics; Sign changes; Totally positive function. Reprints. (kr)