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Prospective Scanning of Events Over Time

AbstractChapter 2 deals with the scan statistic given that a fixed number N of events have occurred at random in a time period. This conditional (on N) case is called retrospective because in typical...

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Number of Clusters: Ordered Spacings

AbstractLet X(1)≤ X(2)≤ ... ≤ X(N) be the ordered values of the X’s where N could be fixed or random.

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Testing for Clustering Superimposed on a Nonuniform Density and Related...

AbstractThe scan statistics presented until now test the null hypothesis of uniformity again a pulse alternative. In this chapter, we modify the scan statistics to detect a cluster superimposed on...

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Scan Statistics for a Sequence of Discrete I.I.D. Variates

AbstractLet X1, X2,...,XN be a sequence of independently and identically distributed (i.i.d.) discrete random variables, where P(Xi= 1) = ρ= 1–P(Xi= 0). We refer to the X’s as a sequence of Bernoulli...

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Scanning Points in a Poisson Process

AbstractLet Yt(w) denote the number of points (X’s) in the interval {t, t + w). The scan statistic \( {S_w} = \mathop {\max }\limits_{0 < t < T - w} \;\{ {Y_t}(w)\}\), denotes the largest number...

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Retrospective Scanning of Events Over Time

AbstractResearchers studying events occurring over a period of time may observe what appears to be a large cluster of events all occurring within a short period of time. The researchers ask whether the...

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Power

AbstractPrevious chapters have almost exclusively dealt with the distribution of the scan statistics under the hypothesis of uniformity. Here we will discuss the computation of power, which requires...

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The Generalized Birthday Problem

AbstractMany researchers deal with data that can be viewed as a series of trials, each with two possible outcomes. We will arbitrarily label the two alternative possible outcomes of a trial as success...

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Scanning N Uniform Distributed Points: Bounds

AbstractIn the study of bounds for scan statistic probabilities two methods have been employed. The first method utilizes the scanning process representation of the scan statistic that has been...

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Approaches Used for Derivations and Approximations

AbstractThis chapter provides background on different approaches, results, and techniques that are used in several of the chapters. Some of the topics: order statistics and direct integration; random...

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Introduction

AbstractIn many fields, decision-makers give great weight to clusters of events. Public Health investigators look for common causal factors to explain clusters of cancer cases or birth defects....

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Erratum to: Approaches Used for Derivations and Approximations

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Erratum to: Scanning N Uniform Distributed Points: Exact Results

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Erratum to: Higher-Dimensional Scans

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Erratum to: Introduction

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Scan Statistics

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Scan Statistics

Abstract Section 43.1 introduces the concept of scan statistics and overviews types used to localize unusual clusters in continuous time or space, in sequences of trials or on a lattice. Section 43.2...

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Approximations and Inequalities for Moving Sums

AbstractIn this article accurate approximations and inequalities are derived for the distribution, expected stopping time and variance of the stopping time associated with moving sums of independent...

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Rutgers University Department of Statistics and Biostatistics

AbstractTime-travel through sixty-five years of statistics at Rutgers. See how the department grew from its early applied roots, its solid trunk of mathematical statistics and probability, to its...

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Research on Probability Models for Cluster of Points Before the Year 1960

AbstractScan statistics describe large number of events or objects clustered close in time or space. A few special cases of scan statistics – long success runs and the sample range – have been widely...

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