Benford's Law and Continuous Dependent Random Variables

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Version 1.0, 16 pages, 1 figure

Scientific paper

Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one would expect if all digits were equally likely, but about 30% of the time. This phenomenon, known as Benford's Law, has many applications, ranging from detecting tax fraud for the IRS to analyzing round-off errors in computer science. The central question is determining which data sets follow Benford's law. Inspired by natural processes such as particle decay, our work examines models for the decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow. The main difficulty is that the resulting random variables are dependent, which we handle by a careful analysis of the dependencies and tools from Fourier analysis to obtain quantified convergence rates.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Benford's Law and Continuous Dependent Random Variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Benford's Law and Continuous Dependent Random Variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Benford's Law and Continuous Dependent Random Variables will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-329646

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.