DOI QR코드

DOI QR Code

ON SOME PROPERTIES OF BENFORD'S LAW

  • Strzalka, Dominik (DEPARTMENT OF DISTRIBUTED SYSTEMS RZESZOW UNIVERSITY OF TECHNOLOGY)
  • Received : 2009.01.28
  • Published : 2010.09.01

Abstract

In presented paper there were studied some properties of Benford's law. The existence of this law in not necessary large sets of numbers is a very interesting example that can show how the complex phenomena can appear in the positional number systems. Such systems seem to be very simple and intuitive and help us proceed with numbers. However, their simplicity in the case of usage in our lifetime is not necessary connected with the simplicity in the case of laws that govern them. Even if this laws indicate the existence of self-similar properties.

Keywords

Benford's law;self-similarity;complex systems

References

  1. F. Benford, The law of anomalous numbers, Proc. Amer. Phil. Soc. 78 (1938), 551-572. (1938)
  2. J. B. Estoup, Les Gammes Stenographiques, Institut Stenographique de France, Paris, 1916.
  3. T. P. Hill, Base-invariance implies Benford’s law, Proc. Amer. Math. Soc. 123 (1995), no. 3, 887-895.
  4. T. P. Hill, The first digit phenomenon, Amer. Sci. 86 (1998), 358-363. https://doi.org/10.1511/1998.31.815
  5. S. Irmay, The relationship between Zipf’s law and the distribution of first digits, J. Appl. Statist. 24 (1997), no. 4, 383-393. https://doi.org/10.1080/02664769723594
  6. J.-M. Jolion, Images and Benford’s law, J. Math. Imaging Vision 14 (2001), no. 1, 73-81. https://doi.org/10.1023/A:1008363415314
  7. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, Calif., 1982.
  8. S. Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), no. 1-4, 39-40. https://doi.org/10.2307/2369148
  9. M. J. Nigrini and L. J. Mittermaier, The use of Benford’s law as an aid in analytical procedures, Auditing: A Journal of Practice and Theory 16 (1997), 52-67.
  10. A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill Companies, 3rd edition, 1991.
  11. H.-O. Peitgen, H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, New York, Springer-Verlag, 1992.
  12. L. Pietronero, E. Tosatti, V. Tosatti, and A. Vespignani, Explaining the uneven distribution of numbers in nature, Physica A 293 (2001), no. 1, 297-304. https://doi.org/10.1016/S0378-4371(00)00633-6
  13. G. K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, 1949.