Regularity of digits and significant digits of random variables

Random Β-expansions with Deleted Digits

In this paper we define random β-expansions with digits taken from a given set of real numbers A = {a1, . . . , am}. We study a generalization of the greedy and lazy expansion and define a function K, that generates essentially all β-expansions with digits belonging to the set A. We show that K admits an invariant measure ν under which K is isomorphic to the uniform Bernoulli shift on A.

Decimal Dust, Significant Digits, and the Search for Stars

The practice of rounding statistical results to two decimal places is one of a large number of heuristics followed in the social sciences. In evaluating this heuristic, the authors conducted simulations to investigate the precision of simple correlations. They considered a true correlation of .15 and ran simulations in which the sample sizes were 60, 100, 200, 500, 1,000, 10,000, and 100,000. T...

Supernumerary Digits of the Hand

Figure 1. Left and right hands with ulnar polysyndactyly. Categorized as type V under the Duran classification.

Handwritten Digits Recognition

Allison mixtures: Where random digits obey thermodynamic principles

Parrondo’s paradox is a well-known situation where losing strategies can be combined to win, and is based on a thermodynamic Brownian ratchet principle. We demonstrate a new extension of Parrondo’s paradox called the Allison mixture where it is possible to paradoxically generate random sequences with nonzero autocovariance, out of subsequences of zero autocovariance. We explain the effect with ...