Abstract

Generation algorithms of record times and values obtained from sequences of independent and non-identically distributed random variables, the distribution functions of which are defined on a common support, are proposed in the present paper. Known algorithms of generation of record times and values are given in Introduction for the case when the initial random variables are independent and identically distributed. A brief review of the scientific literature associated with this topic is also given in Introduction. It is also pointed out there that all efficient algorithms of record generation are based on the Markov property of records. In Section 2, the distribution functions of record times and values are derived for the case when the initial random variables are independent and non-identically distributed. The corresponding record-generation algorithms are proposed for the first time. These algorithms are based on the derived distributions and the Markov property of records, which also holds in the case when the initial observations are independent but non-identically distributed. At the end of this work, in Section 3, the proposed algorithms are tested by simulation experiments. In these experiments the records are generated for the case when the initial random variables have Gumbel distribution functions.

中文翻译：

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从独立和非同分布变量的序列获得的记录的生成

摘要

本文提出了从独立和非同分布的随机变量序列获得记录时间和值的生成算法，其分布函数定义在公共支持上。在引言中针对初始随机变量独立同分布的情况给出了已知的记录时间和值的生成算法。引言中还简要回顾了与该主题相关的科学文献。那里还指出，所有有效的记录生成算法都是基于记录的马尔可夫性质。在第二节中，针对初始随机变量独立且非同分布的情况导出了记录时间和值的分布函数。首次提出了相应的记录生成算法。这些算法基于导出的分布和记录的马尔可夫属性，这也适用于初始观测值独立但分布不同的情况。在这项工作的最后，在第 3 节中，所提出的算法通过模拟实验进行了测试。在这些实验中，记录是针对初始随机变量具有 Gumbel 分布函数的情况生成的。