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On numbers of observations in random regions determined by records
Statistics ( IF 1.9 ) Pub Date : 2020-06-30 , DOI: 10.1080/02331888.2020.1786091
Anna Dembińska 1 , Masoumeh Akbari 2 , Jafar Ahmadi 3
Affiliation  

Near-record observations are the ones that occur between successive record times and within a fixed distance of the current record value. In this paper, the concept of near-record observations is generalized to the notion of observations that fall into a random region determined by a given record and a Borel set. Description of the distribution of the number of such observations is provided, and asymptotic behaviour of this number is investigated. In addition, some applications of the new results to derive exact and asymptotic properties of inter-record times and of numbers of repetitions of records are presented.

中文翻译:

关于由记录确定的随机区域中的观察数量

近记录观测是在连续记录时间之间和当前记录值的固定距离内发生的观测。在本文中,近记录观测的概念被推广到观测落入由给定记录和 Borel 集确定的随机区域的概念。提供了此类观察数量分布的描述,并研究了该数量的渐近行为。此外,还介绍了新结果的一些应用,以推导出记录间时间和记录重复次数的精确和渐近特性。
更新日期:2020-06-30
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