Approximation for the Distribution of Three-dimensional Discrete Scan Statistic

2013/03/15 by Alexandru Amărioarei, Amarioarei, Alexandru, Cristian Preda +2
Chemistry · Computer Science · Decision Sciences · Mathematics · Medicine · #62E17 #62M30 #Advanced Proteomics Techniques and Applications #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #Computation (stat.CO) #Data-Driven Disease Surveillance #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #math.PR #msc:62E17 #msc:62M30 #stat.CO

paper · pdf · doi:10.48550/arxiv.1303.3775

arxiv created 2013/03/15 · openalex publication_date 2013/03/15 · arxiv updated 2013/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan statistics. Importance sampling algorithm is used to obtains sharp bounds for the simulation error. Simulation results and comparisons with other approximations are presented for the binomial and Poisson models.

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