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...
View ArticleNumber 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.
View ArticleTesting 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...
View ArticleScan 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...
View ArticleScanning 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...
View ArticleRetrospective 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...
View ArticlePower
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...
View ArticleThe 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...
View ArticleScanning 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...
View ArticleApproaches 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...
View ArticleIntroduction
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....
View ArticleScan 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...
View ArticleApproximations 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...
View ArticleRutgers 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...
View ArticleResearch 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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