Bounds on the Expectations of $$\boldsymbol{L}$$ -Statistics Based on iid Life Distributions

IF 0.8 Q3 STATISTICS & PROBABILITY

Mathematical Methods of Statistics Pub Date : 2022-09-28 DOI:10.3103/s1066530722020041

Tomasz Rychlik

引用次数: 0

Abstract

We consider the order statistics based on independent identically distributed non-negative random variables. We determine sharp upper bounds on the expectations of arbitrary linear combinations of order statistics, expressed in the scale units being the $p$th roots of $p$th raw moments of original variables for various $p\geq 1$. The bounds are more precisely described for the single order statistics and spacings. The lower bounds are concluded from the upper ones.

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$$\boldsymbol{L}$$期望值的界限——基于id寿命分布的统计

摘要考虑基于独立同分布非负随机变量的序统计量。我们确定了有序统计量的任意线性组合的期望的明显上界，以尺度单位表示为$p$的根$p$原始变量的原始矩对于各种$p\geq 1$。对于单阶统计量和间隔，边界更精确地描述。下界是由上界推导出来的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.