Limit theorems for runs containing two types of contaminations. Paper with detailed proofs
Probability
2023-12-19 v2
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.
Keywords
Cite
@article{arxiv.2309.11602,
title = {Limit theorems for runs containing two types of contaminations. Paper with detailed proofs},
author = {István Fazekas and Borbála Fazekas and Michael Ochieng Suja},
journal= {arXiv preprint arXiv:2309.11602},
year = {2023}
}
Comments
25 pages, 8 figures