\(r\)-scan statistics of a marker array in multiple sequences derived from a common progenitor.
type: Item
instance of: scholarly article
title: \(r\)-scan statistics of a marker array in multiple sequences derived from a common progenitor.
zbMATH Open document ID: 1084.92506
author: Chingfer Chen
author: Samuel Karlin
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aoap/1019487507
review text: This study is motivated by problems of molecular sequence comparisons for biological traits conserved or lost over evolution time. A marker of interest is distributed in the genome of the ancestor and inherited among \(l\) offspring species which descend from this common ancestor. Each marker will be retained or lost during the evolution of the descendent species. The objective of the analysis here is to ascertain probabilities of clustering or overdispersion of the marker array among the sequences of the descendent species. Limiting distributions for the extremal \(r\)-scan statistics (defined in text) of the trait distributed among the \(l\) dependent offspring processes are derived by adapting the Chen-Stein Poisson approximation method. Results that accommodate new occurrences of the trait (gene) arising from duplications and transposition occurrences are also described.The \(r\)-scan statistical analysis is further applied to a multi sequence combined Poisson model where \({B_1,\dots, B_l}\) are generated from \(m\) independent Poisson processes \({A_1,\dots, A_m}\) such that \(B_k = \bigcup_{i\epsilon Z_k}A_i\), where \({Z_k}_1\leq k\leq l\) are subsets of \({1, 2,\dots,m}\).
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 1906273
zbMATH Keywords: r-scan statistics
zbMATH Keywords: Chen-Stein Poisson approximation
zbMATH Keywords: Poisson processes
zbMATH Keywords: total variation distance
zbMATH Keywords: asymptotic distributions
MaRDI profile type: Publication
OpenAlex ID: W2039244956
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DOI: 10.1214/AOAP/1019487507
description: scientific article; zbMATH DE number 1906273