矩限制下次序统计量均值的界

设X_1 X_2…,X_n为随机变量,它们的次序统计量为X_(14)A≤X_(26a)≤…≤X_(n.n),记E(X_(itn))=μ_(iln),当X_1…,X_n有共同的均值μ,方差σ~2时,〔1〕中得出了其次序统计量均值的界,本文在E(X_i)=μ,E|X_i|p=c<∞(p>1)时,得出了相应的结果。特别,如对任p>1.E|X_i|p=c(p)≤k<∞,i=1,2,…时,我们得出

Bounds on Expctations of Order Statisticsunder Moment Restrictions

Let X_1…, X_nbe random variables with the corresponding order statistic denoted by X_(1:n)≤X_(2:n)≤…≤X_(a:a) Arnold and Groenveld studied the bound of expectations of the orderd statistics when EX_i=μ and var(X_i)=σ~2. Ins the paper, we obtain similer results when EX_i=μ and E|X_1|p<∞ for some P>1 Especially, if E|X|=C(p)≤K<∞ for i=1,…, n and any p>1, we hav where μkin=E(X_(k:n)), k=1,…, n