Upper Bounds for the Expected Maxima of Independent Random Variables Given Known First Four Moments

被引:0
作者
Ivanov, D., V [1 ]
机构
[1] Lomonosov Moscow State Univ, Moscow 119991, Russia
关键词
expectation of the maximum; reachability of boundaries; Holder's inequality; Lagrange multiplier method; ORDER-STATISTICS; EXPECTATIONS;
D O I
10.1134/S0001434621090017
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The paper is devoted to the study of conditional bounds for the expectation of the maximum of independent identically distributed standardized random variables for which the values of the skewness and kurtosis coefficients are known. With the aid of Holder's inequality, an upper bound (in the form of a lower bound for a certain expression with parameters) is obtained and a criterion for the reachability of this estimate is formulated. A lower bound for the upper boundary of the expectation of the maximum is also found. A simpler and rougher upper bound is given in explicit form.
引用
收藏
页码:311 / 321
页数:11
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