arXiv subjects

Michael Ochieng Suja

Publications and source records attributed to Michael Ochieng Suja.

2 recordsLinked to original sources

arXiv2023

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

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.

math.PR↗

arXiv2023

Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs

We study the length of $T$-contaminated runs of heads in the well-known coin tossing experiment. A $T$-contaminated run of heads is a sequence of consecutive heads interrupted by $T$ tails. For $T=1$ and $T=2$ we find the asymptotic distribution for the first hitting time of the $T$ contaminated run of heads having length $m$; furthermore, we obtain a limit theorem for the length of the longest $T$-contaminated head run. We prove that the rate of the approximation of our accompanying distribution for the length of the longest $T$-contaminated head run is considerably better than the previous ones. For the proof we use a powerful lemma by Csáki, Földes and Komlós.

math.PR↗