Maximum-entropy distributions having prescribed first and second moments (Corresp.)

摘要: The entropy H of an absolutely continuous distribution with probability density function p(x) is defined as = - \int \log dx . formal maximization , subject to the moment constraints x^r \mu_r, r 0,1,\cdots,m leads \exp (- \sum_{r=0}^m \lamnbda_r x^r) where \lambda_r have be chosen so satisfy constraints. Only case m 2 considered. It shown that when x has finite range, a maximizing exists and unique. When range [0,\infty) maximum-entropy if, only \mu_2 \leq \mu_1^2 table given which enables computed. > discussed in some detail.