摘要
定义n(n≥2)个正实数x1,x2,…,xn的r阶方差平均Dr(x,p)(x,p∈Rn++,r≥2).证明了:1.min{x}≤Dr(x,p)≤max{x};2.若正整数r>3,则有Dr(x,p)≥D3(x,p);3.若正整数r≥3,则有Dr(x,p)≥2/r1/(r-2)A(x,p),并且系数2/r1/(r-2)是最佳的.此处A(x,p)=∑nk=1pkxk∑nk=1pk为x1,x2,…,xn的带权系数p的加权算术平均.
The mean D_r(x,p) of variance of order r is defined for n(n≥2) positive real numbers (x_1,x_2,…,x_n,)where x,p∈R^n_(++),r≥2. The authors main results are:1. min ｛x｝≤D_r(x,p)≤max｛x｝; 2. if the positive integral number r>3,then D_r(x,p)≥D_3(x,p); 3. if the positive integral number r≥3,then D_r(x,p)≥(2/r)^(1/(r-2))A(x,p),and the constant (2/r)^(1/(r-2)) is the best possibility, where A(x,p) is the arithmetic mean of x with weight p.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第6期1011-1018,共8页
Journal of Sichuan University(Natural Science Edition)
关键词
方差平均
r阶方差
数学期望
HERMITE矩阵
mean of variance
variance of order r
mathematical expectation
Hermitian matrix
