Please use this identifier to cite or link to this item: https://doi.org/10.1534/g3.120.401575
Title: A faster and more accurate algorithm for calculating population genetics statistics requiring sums of stirling numbers of the first kind
Authors: Chen, S.L. 
Temme, N.M.
Keywords: Asymptotic analysis
Cumulative distribution functions
Evolutionary inference
Numerical algorithms
Population genetics statistics
Stirling numbers of the first kind
Issue Date: 2020
Publisher: Genetics Society of America
Citation: Chen, S.L., Temme, N.M. (2020). A faster and more accurate algorithm for calculating population genetics statistics requiring sums of stirling numbers of the first kind. G3: Genes, Genomes, Genetics 10 (11) : 3959-3967. ScholarBank@NUS Repository. https://doi.org/10.1534/g3.120.401575
Rights: Attribution 4.0 International
Abstract: Ewen's sampling formula is a foundational theoretical result that connects probability and number theory with molecular genetics and molecular evolution; it was the analytical result required for testing the neutral theory of evolution, and has since been directly or indirectly utilized in a number of population genetics statistics. Ewen's sampling formula, in turn, is deeply connected to Stirling numbers of the first kind. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu's Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed. Copyright © 2020 Chen, Temme
Source Title: G3: Genes, Genomes, Genetics
URI: https://scholarbank.nus.edu.sg/handle/10635/199418
ISSN: 21601836
DOI: 10.1534/g3.120.401575
Rights: Attribution 4.0 International
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