An Approach to Computations Involving Spacings with Applications to the Scan Statistic

doi:10.1007/978-1-4612-1578-3_6

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Title:	An Approach to Computations Involving Spacings with Applications to the Scan Statistic
Authors:	Huffer, Fred W.;Lin, Chien-tai
Contributors:	淡江大學數學學系
Keywords:	Uniform distribution;Number of clumps;Order statistics;m-spacings;Syblolic computation
Date:	1999
Issue Date:	2010-01-28
Publisher:	Boston: Birkhäuser
Abstract:	Consider the order statistics fromNi.i.d. random variables uniformly distributed on the interval (0,1]. We present a general method for computing probabilities involving differences of the order statistics or linear combinations of the spacings between the order statistics. This method is based on repeated use of a basic recursion to break up the joint distribution of linear combinations of spacings into simpler components which are easily evaluated. LetS w denote the (continuous conditional) scan statistic with window length w. Let Cwdenote the number of m: w clumps among theNrandom points, where an m: w clump is defined as m points falling within an interval of length w. We apply our general method to compute the distribution ofS w (for smallN)and the lower-order moments of Cw. The final answers produced by our approach are piecewise polynomials (in w) whose coefficients are computed exactly. These expressions can be stored and later used to rapidly compute numerical answers which are accurate to any required degree of precision.
Relation:	Scan Statistics and Applications, pp.141-163
DOI:	10.1007/978-1-4612-1578-3_6
Appears in Collections:	[Graduate Institute & Department of Mathematics] Chapter

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