Titlebook: Handbook of Scan Statistics; Joseph Glaz,Markos V. Koutras Reference work 2024 Springer Science+Business Media, LLC, part of Springer Natu

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Frosso S. Makri,Zaharias M. Psillakisgulation is a collection of triangles satisfying certain adjacency conditions. To give a rigorous definition of a triangulation it is helpful to define the notion of a simplex and of a simplicial complex. It does no harm to define these notions in any dimension.

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Anant Godbole,Katherine Grzesik,Heather Shappelly abelian groups. Using this result, we define the Betti numbers. We state the fundamental fact that if two complexes have the same geometric realization, then these complexes and their geometric realization have the same homology groups. We also show how the Euler–Poincaré characteristic of a compl

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Research on Probability Models for Cluster of Points Before the Year 1960,s and the sample range – have been widely applied and their distributions known for hundreds of years. Most of the theory on the probability of scan statistics was developed after 1960. Prior to 1960, researchers in various fields have used scan statistics and were either limited to the special case

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Approximations for Discrete Scan Statistics on i.i.d and Markov-Dependent Bernoulli Trials,i trials. The approximations are developed using the finite Markov chain imbedding technique of Fu and Koutras (J Am Stat Assoc 89(427):1050–1058, 1994) and the methods in Fu and Johnson (Adv Appl Probab 41(1):292–308, 2009) and Koutras and Milienos (J Stat Plann Inference 142(6):1464–1479, 2012). T

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Demimartingale Approaches for ScanStatistics,r of successes. The main objective of this contribution is to serve as a self-contained source of some recent results concerning both the simple and the multiple scan statistic. These results are innovative in the sense that they seem to be the first ones on scan statistics that were derived by mean

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