极值偏差下的吉布斯条件定理

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2022-11-07 DOI:10.1137/s0040585x97t991015

M. Biret, M. Broniatowski, Z. Cao

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引用次数: 0

摘要

概率论及其应用，67卷，第3期，389-414页，2022年11月。研究了独立同分布(i.i.d)样本在其和的大超出下的条件分布的一些性质。与经典情况相比，当条件作用事件在较大偏差范围内时，观察到求和的渐近独立性的阈值。本文是Broniatowski和Cao [Extremes, 17 (2014)， pp. 305—336]的延伸。工具包括一个新的Edgeworth扩展，适用于特定的三角形数组，其中行是由具有发散参数的倾斜分布产生的，以及一些阿贝尔类型的结果。

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A Gibbs Conditional Theorem under Extreme Deviation

Theory of Probability &Its Applications, Volume 67, Issue 3, Page 389-414, November 2022.
We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao [Extremes, 17 (2014), pp. 305--336]. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.

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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.