Aaron Carl Smith | Searcharxiv

arXiv2013

Benford-Newcomb Subsequences for Fraud Detection

Benford's law is frequently used to evaluate the likihood that data is misrepresentative. Typically statistical tests measure the likihood. Another method of employing Benford's law is to compare the frequency of leading digits to the probabilities of leading digits over a subset of the natural numbers. This paper proposes using the probabilities of leading digits from uniform, natural numbers to establish interval criteria for when to look more closely into the possibility of misrepresentative data.

math.ST↗

arXiv2012

Using Householder Matrices to Establish Mixing Test Critical Values

A measure-preserving dynamical system can be approximated by a Markov shift with a bistochastic matrix. This leads to using empirical stochastic matrices to measure and estimate properties of stirring protocols. Specifically, the second largest eigenvalue can be used to statistically decide if a stirring protocol is weak-mixing, ergodic, or nonergodic. Such hypothesis tests require appropriate probability distributions. In this paper, we propose using Monte Carlo empirical probability distributions from unistochastic matrices to establish critical values. These unistochastic matrices arise from randomly constructed Householder matrices.

math.DS↗