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VOL. 45 | 2004 $r$-scan extremal statistics of inhomogeneous Poisson processes


Studies of inhomogeneities in long DNA sequences can be insightful to the organization of the human genome (or any genome). Questions about the spacings of a marker array and general issues of sequence heterogeneity in our studies of DNA and protein sequences led us to statistical considerations of $r$-scan lengths, the distances between marker $i$ and marker $i+r$, $i=1,2,3,\ldots\,$. It is interesting to characterize the $r$-scan lengths harboring clusters or indicating regions of over-dispersion of the markers along the sequence. Applications are reviewed for certain words in the Haemophilus genome and the Cyanobacter genome.


Published: 1 January 2004
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62141
MathSciNet: MR2126904

Digital Object Identifier: 10.1214/lnms/1196285397

Primary: 92B05 , 92D20

Keywords: $r$-scan statistics , Asymptotic distributions , inhomogeneous Poisson marker array

Rights: Copyright © 2004, Institute of Mathematical Statistics


Vol. 45 • 1 January 2004
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