设ｘ１，ｘ２，…ｘｎ（连续未知），Ｆｎ为经验分布函数，Ｈｎ（ｘ）为随机加权经验分布函数，。ｘｎ１≤ｘｎ２≤…≤ｘｎｎ为次序统计量．记以Ｆｎ取代σ２（Ｊ，Ｆ）中的Ｆ即得σ２（Ｊ，Ｆｎ）．

Suppose x1, x2''', xn F. Let Fn be the empirical distribution function, Hn(x) be the random weighting empirical distribution .function and xn1≤xn2≤''' ≤xnn be the order statistics of x1,x2,''',xn. Put Tn(Hn) = xJ(F(x)) dF(x). In this paner, the following fomulasare proved when J(.) satisfies some conditions and,σ2(J, Fn) is defined analogously, P represents the conditional probability given x1, x2,''. xn.