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Benford’s law, its applicability and breakdown in the IR spectra of polymers

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  • Bormashenko, Ed.
  • Shulzinger, E.
  • Whyman, G.
  • Bormashenko, Ye.

Abstract

Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra is random. This observation may be explained by the fact that the value of transmittance Tr is restricted 0

Suggested Citation

  • Bormashenko, Ed. & Shulzinger, E. & Whyman, G. & Bormashenko, Ye., 2016. "Benford’s law, its applicability and breakdown in the IR spectra of polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 524-529.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:524-529
    DOI: 10.1016/j.physa.2015.10.090
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    References listed on IDEAS

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    1. Mir, T.A., 2012. "The law of the leading digits and the world religions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 792-798.
    2. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
    3. James L Friar & Terrance Goldman & Juan Pérez–Mercader, 2012. "Genome Sizes and the Benford Distribution," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    4. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
    5. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
    6. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    7. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
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    Cited by:

    1. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    2. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    3. da Silva, A.J. & Floquet, S. & Santos, D.O.C. & Lima, R.F., 2020. "On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).

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