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arXiv · 2309.11602

Limit theorems for runs containing two types of contaminations. Paper with detailed proofs

István Fazekas·Borbála Fazekas·Michael Ochieng Suja
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Abstract

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 1 failure of type I and at most 1 failure of type II. The limiting distribution of the first hitting time and the accompanying distribution for the length of the longest at most 1+1 contaminated run are obtained. This paper contains the detailed mathematical proofs. Simulation results supporting the theorems are also presented.

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István Fazekas, Borbála Fazekas, Michael Ochieng Suja. 2023-09-20. Limit theorems for runs containing two types of contaminations. Paper with detailed proofs. https://arxiv.org/abs/2309.11602

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