Abstract

In this paper, an expression for computing the Pearson’s correlation coefficient between the random upper record value, $X$ and the random number of observations, $Y$ is obtained. Also derived are theoretical results for the joint bivariate probability function (pf) of $X$ and $Y,$ their marginal pf, and an alternate expression (to the correlation coefficient) measuring their dependence, where the support for $X$ depends on an unknown threshold and an terminal parameter. Furthermore, some distributional properties are presented. The results are new to the literature on upper record value and interesting from the practicality and usefulness of upper record values. Analogous results for the lower record value are made available in another article. The concept and the derived expressions are illustrated using the recorded radiation levels in a nuclear disaster on March 2011 at Fukushima, Japan.

摘要

在本文中，计算随机上记录值之间的皮尔逊相关系数的表达式，$X$和观察的随机数，$是$获得。还导出了联合双变量概率函数 (pf) 的理论结果$X$和$是,$它们的边际 pf 和一个替代表达式（相关系数）测量它们的依赖性，其中支持$X$取决于未知阈值和终端参数。此外，还提出了一些分布特性。这些结果对于关于上记录值的文献来说是新的，并且从上记录值的实用性和有用性来看很有趣。在另一篇文章中提供了较低记录值的类似结果。使用 2011 年 3 月在日本福岛发生的核灾难中记录的辐射水平来说明该概念和派生表达式。