Using Moments to Approximate the Distribution of the Scan Statistic

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Title:	Using Moments to Approximate the Distribution of the Scan Statistic
Authors:	Huffer, Fred W.;Lin, Chien-tai
Contributors:	淡江大學數學學系
Keywords:	Compound Poisson approximation;Markov chain approximation;linear programming;probability bounds;method of moments;spacings;number of clumps
Date:	1999
Issue Date:	2010-01-28
Publisher:	Boston: Birkhäuser
Abstract:	Let C w denote the number ofm:wclumps amongNrandom points uniformly distributed in the interval (01]. (We say that anm:wclump exists whenmpoints fall within an interval of lengthw.) The previous chapter described how to compute the lower-order moments ofC w . In the present chapter, we discuss ways these moments can be used to obtain bounds and approximations for the distribution of the (continuous conditional) scan statisticS w . We give upper and lower bounds based on the use of four moments. In some situations, these bounds improve considerably on the previously available bounds. We present an approximation based on a simple Markov chain model, and also give a variety of compound Poisson approximations. These approximations are compared with others in the literature. Finally, we present a compound Poisson approximation to the distribution of the number of clumpsC w .
Relation:	Scan Statistics and Applications, pp.165-190
Appears in Collections:	[Department of Applied Mathematics and Data Science] Chapter

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