^{1}Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA ^{2}Accounting and Information Systems, School of Business, The College of New Jersey, Ewing, NJ 08628, USA

Received 2 June 2008; Revised 6 September 2008; Accepted 13 October 2008

Fix a base B>1 and let ζ have the standard exponential
distribution; the distribution of digits of ζ base B is
known to be very close to Benford's law. If there exists a C such
that the distribution of digits of C times the elements of some set is the same as that of ζ, we say that set exhibits
shifted exponential behavior base B. Let X1,…,XN be i.i.d.r.v. If the Xi's are Unif, then as N→∞ the distribution
of the digits of the differences between adjacent order statistics
converges to shifted exponential behavior. If instead Xi's come from a compactly supported distribution with uniformly bounded first and second derivatives and a second-order Taylor series expansion at each point, then the distribution of digits of any Nδ consecutive differences and all N−1 normalized
differences of the order statistics exhibit shifted exponential behavior.
We derive conditions on the probability density which determine
whether or not the distribution of the digits of all the
unnormalized differences converges to Benford's law, shifted exponential behavior, or oscillates between the two, and show that the Pareto distribution leads to oscillating behavior.