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 \(1+1\) $1+1$ 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 \(1+1\) $1+1$ 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.