## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### $r$-scan extremal statistics of inhomogeneous Poisson processes

#### Abstract

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

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

Dates
First available in Project Euclid: 28 November 2007

https://projecteuclid.org/euclid.lnms/1196285397

Digital Object Identifier
doi:10.1214/lnms/1196285397

Mathematical Reviews number (MathSciNet)
MR2126904

Zentralblatt MATH identifier
1268.62141

Rights
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. https://projecteuclid.org/euclid.lnms/1196285397