Institute of Mathematical Statistics Lecture Notes - Monograph Series

$r$-scan extremal statistics of inhomogeneous Poisson processes

Samuel Karlin and Chingfer Chen

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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.

Chapter information

Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 287-290

First available in Project Euclid: 28 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92B05: General biology and biomathematics 92D20: Protein sequences, DNA sequences

$r$-scan statistics inhomogeneous Poisson marker array asymptotic distributions

Copyright © 2004, Institute of Mathematical Statistics


Karlin, Samuel; Chen, Chingfer. $r$-scan extremal statistics of inhomogeneous Poisson processes. A Festschrift for Herman Rubin, 287--290, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285397.

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