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The Exact Distribution of Divergence Times

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Abstract

The recent work of Haubold and Wiehe (Mol. Biol. Evol. 18:1157–1160, 2001) considered statistical inference of the divergence time. However, there appears to be a fundamental flaw in the paper since it treated the divergence time as a random variable and not as a parameter. In this note, we derive a valid statistical inference for the divergence time. We derive an estimator for the divergence time as well as explicit expressions for its the probability density function, cumulative distribution function and the means. We also provide a 5-line computer program for computing the associated confidence intervals. We expect that the results presented could be useful for statistical modeling of divergence times.

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References

  • Haubold, B., Wiehe, T., 2001. Statistics of divergence times. Mol. Biol. Evol. 18, 1157–1160.

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  • Johnson, N.L., Kotz, S., Balakrishnan, N., 1994. Continuous Univariate Distributions, 2nd edn., vol. 1. Wiley, New York.

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  • Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I., 1986. Integrals and Series, vol. 2. Gordon and Breach Science Publishers, Amsterdam.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M60 1QD, UK

    Saralees Nadarajah

  2. Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC, 20052, USA

    Samuel Kotz

Authors
  1. Saralees Nadarajah
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  2. Samuel Kotz
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Correspondence to Saralees Nadarajah.

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Nadarajah, S., Kotz, S. The Exact Distribution of Divergence Times. Bull. Math. Biol. 70, 635–640 (2008). https://doi.org/10.1007/s11538-007-9272-3

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  • DOI: https://doi.org/10.1007/s11538-007-9272-3

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