包含两类污染的运行极限定理

Pub Date : 2024-07-06 DOI:10.1007/s10998-024-00600-6

István Fazekas, Borbála Fazekas, Michael Ochieng Suja

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引用次数: 0

摘要

本文研究了具有三种结果的试验序列。这些结果被标记为成功、I 型失败和 II 型失败。如果一个序列中最多包含一次 I 型失败和一次 II 型失败，那么这个序列就被称为 "最多（1+1）污染 "序列。由此可以得到最长的最多（1+1）次污染运行的长度分布。证明基于 Csáki、Földes 和 Komlós 的一个强大的lemma。除了数学证明外，还给出了支持我们定理的模拟结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A limit theorem for runs containing two types of contaminations

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A limit theorem for runs containing two types of contaminations

In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most \(1+1\) contaminated, if it contains at most one failure of type I and at most one failure of type II. The accompanying distribution for the length of the longest at most \(1+1\) contaminated run is obtained. The proof is based on a powerful lemma of Csáki, Földes and Komlós. Besides a mathematical proof, simulation results supporting our theorem are also presented.

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