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 .
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Huffer, F.W., Lin, CT. (1999). Using Moments to Approximate the Distribution of the Scan Statistic. In: Glaz, J., Balakrishnan, N. (eds) Scan Statistics and Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1578-3_7
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DOI: https://doi.org/10.1007/978-1-4612-1578-3_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7201-4
Online ISBN: 978-1-4612-1578-3
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