Journal of Theoretical Probability 21(1), pp. 97-117.
ISSN/ISBN: 0894-9840 DOI: Not available at this time.
Abstract: In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to a conversion from dollars to euros) changes the distribution of the mantissas, or fraction parts, of the data. A scaledistortion factor for probability distributions is defined, based on the Kantorovich distance between distributions. Sharp lower bounds are found for the scale-distortion of n-point data sets, and the unique data set of size n with the least scale-distortion is identified for each positive integer n. A sequence of real numbers is shown to follow Benfordâ€™s Law (base b) if and only if the scale-distortion (base b) of the first n data points tends zero as n goes to infinity. These results complement the known fact that Benfordâ€™s Law is the unique scale-invariant probability distribution on mantissas.
Bibtex:
@article {,
AUTHOR = {Berger, Arno and Hill, Theodore P. and Morrison, Kent},
TITLE = {Scale-Distortion Inequalities for Mantissas of Finite Data Sets},
JOURNAL = {Journal of Theoretical Probability},
VOLUME = {21},
NUMBER = {1},
YEAR = {2008},
PAGES = {97--117},
ISSN = {0894-9840},
}
Reference Type: Journal Article
Subject Area(s): Probability Theory