Distributions of homogeneous means of uniform independent random variables and a characterization of means

摘要

Let U, V be two independent random variables uniformly distributed in (0, 1] and let M be a symmetric increasing and homogeneous mean. A general formula for the distribution function of the random variable is presented. Under some regularity assumptions, applying this formula, the implication F_M(U,V) = F_N(U,V) => M = N, (a characterization of means) is proved. Given a distribution function F, the integro-functional equation is considered. An application is provided.