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Corpus ID: 119329600

Notes on scale-invariance and base-invariance for Benford's Law

@article{Wojcik2013NotesOS,
title={Notes on scale-invariance and base-invariance for Benford's Law},
author={M. R. W'ojcik},
journal={arXiv: Probability},
year={2013}
}

It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable approximation to a continuous random variable) so that if X and Y+X are equally distributed modulo 1 and Y is independent of X then X is uniformly distributed modulo 1 (or approximates the uniform distribution equally reasonably). This translates into a… CONTINUE READING