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Products of random variables and the first digit phenomenon

Author

Listed:
  • Chenavier, Nicolas
  • Massé, Bruno
  • Schneider, Dominique

Abstract

We provide conditions on dependent and on non-stationary random variables Xn ensuring that the mantissa of the sequence of products ∏1nXk is almost surely distributed following Benford’s law or converges in distribution to Benford’s law. This is achieved through proving new generalizations of Lévy’s and Robbins’s results on distribution modulo 1 of sums of independent random variables.

Suggested Citation

  • Chenavier, Nicolas & Massé, Bruno & Schneider, Dominique, 2018. "Products of random variables and the first digit phenomenon," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1615-1634.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:5:p:1615-1634
    DOI: 10.1016/j.spa.2017.08.003
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