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First Digit Oscillations

Author

Listed:
  • Don Lemons

    (Department of Physics, Bethel College, North Newton, KS 67117, USA
    These authors contributed equally to this work.)

  • Nathan Lemons

    (Los Alamos National Laboratory, Los Alamos, NM 87545, USA
    These authors contributed equally to this work.)

  • William Peter

    (John Hopkins Applied Physics Laboratory, Laurel, MD 20723, USA
    These authors contributed equally to this work.)

Abstract

The frequency of the first digits of numbers drawn from an exponential probability density oscillate around the Benford frequencies. Analysis, simulations and empirical evidence show that datasets must have at least 10,000 entries for these oscillations to emerge from finite-sample noise. Anecdotal evidence from population data is provided.

Suggested Citation

  • Don Lemons & Nathan Lemons & William Peter, 2021. "First Digit Oscillations," Stats, MDPI, vol. 4(3), pages 1-7, July.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:3:p:35-601:d:588581
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    References listed on IDEAS

    as
    1. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
    2. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    3. Steven J. Miller & Mark J. Nigrini, 2008. "Order Statistics and Benford's Law," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-19, December.
    Full references (including those not matched with items on IDEAS)

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