1. A Faster and More Accurate Algorithm for Calculating Population Genetics Statistics Requiring Sums of Stirling Numbers of the First Kind
- Author
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Swaine L. Chen, Nico M. Temme, and Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands
- Subjects
FOS: Computer and information sciences ,Numerical algorithms ,G.0 ,G.1 ,Stirling numbers of the first kind ,Asymptotic analysis ,Population genetics ,Improved method ,Cumulative distribution functions ,QH426-470 ,Software and Data Resources ,11B73, 92D20, 41A60, 65D20 ,01 natural sciences ,Methodology (stat.ME) ,010104 statistics & probability ,03 medical and health sciences ,Evolutionary inference ,Statistics ,Genetics ,Stirling number ,0101 mathematics ,Molecular Biology ,Genetics (clinical) ,Statistics - Methodology ,Statistic ,030304 developmental biology ,Mathematics ,Probability ,0303 health sciences ,Cumulative distribution function ,Estimator ,Genetics, Population ,Population genetics statistics ,Algorithm ,Algorithms - Abstract
Stirling numbers of the first kind are used in the derivation of several population genetics statistics, which in turn are useful for testing evolutionary hypotheses directly from DNA sequences. 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 $F_s$. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed., 17 pages, 8 figures
- Published
- 2020
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