Asymptotic results for the multiple scan statistic

Abstract

The contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at least r successes among them (r≤k≤n). In this paper we establish some asymptotic results for the distribution of the multiple scan statistic, as n,k,r→∞ and illustrate their accuracy through a simulation study. Our approach is based on an appropriate combination of compound Poisson approximation and random walk theory.

Approximating the Distribution of the Multiple Scan Statistic

“…1, the compounding cumulative distribution function G does not admit an explicit closed form, and, therefore, the task of calculating approximations and the asymptotic distribution of W n;k;r is difficult. Boutsikas et al (2017) motivated by this problem provided an approximation to G. To be more specific, let r; k ! 1 so that r=k !…”