关于期望评价的一个例子

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2024-08-14 DOI:10.1137/s0040585x97t991933

A. V. Bulinski

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引用次数: 0

摘要

概率论及其应用》第 69 卷第 2 期第 313-321 页，2024 年 8 月。我们研究（可能）独立随机变量 $\xi_1,\dots,\xi_n$ 序列中最大元素 $\overline{\xi}_n$ 的分布。研究考虑了基于量子函数的随机变量期望值评估公式。该公式被应用于通过分布函数变换的随机变量的非递减函数的期望值评估。分布函数不连续的情况最为有趣。作为推论，我们完善了作者前一篇文章[《理论概率应用》，68 (2023)，第 392--410 页]中提出的一个例子。

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On an Example of Expectation Evaluation

Theory of Probability &Its Applications, Volume 69, Issue 2, Page 313-321, August 2024.
We study the distribution of the maximal element $\overline{\xi}_n$ of a sequence of (possibly) independent random variables $\xi_1,\dots,\xi_n$. A formula for evaluation of a random variable expectation based on a quantile function is considered. This formula is applied to evaluation of the expectation for a nondecreasing function of a random variable transformed via its distribution function. The case of a discontinuous distribution function is the most interesting. As a corollary, we refine an example proposed in the author's previous article [Theory Probab. Appl., 68 (2023), pp. 392--410].

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来源期刊

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.