Approximation for the distribution of extremes of one dependent stationary sequences of random variables

TL;DR

This paper enhances the approximation methods for the distribution of extremes in 1-dependent stationary sequences, broadening applicability and reducing errors, with an application to scan statistics in Bernoulli trials.

Contribution

It introduces improved approximation techniques for the distribution of extremes in dependent sequences, extending previous results and providing practical applications.

Findings

Broadened the applicability of existing approximation methods.

Reduced the approximation error in the distribution of extremes.

Applied results to scan statistics in Bernoulli trials.

Abstract

In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation error. An application to the study of the distribution of scan statistics generated by Bernoulli trials is given.