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A Statistical Derivation of the Significant-Digit Law
  • T. Hill
  • Computer Science
  • 1 November 1995
TLDR
If distributions are selected at random (in any "unbi- ased" way) and random samples are then taken from each of these dis- tributions, the significant digits of the combined sample will converge to the logarithmic (Benford) distribution.
Comparisons of Stop Rule and Supremum Expectations of I.I.D. Random Variables
Implicitly defined (and easily approximated) universal constants 1.1 < an random variables and if Tn is the set of stop rules for Xl, "', Xn, then E(max{Xl , • • • ,Xn}) ~ an sup {EX, : tE Tn}, and
Base-Invariance Implies Benford's Law
A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only baseinvariant distributions are shown to be convex combinations of
Strong laws for L- and U-statistics
Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) and for U-statistics (averages of kernels of random samples) for ergodic stationary processes,
Prophet inequalities and order selection in optimal stopping problems
A complete determination is made of the possible values for E(sup X") and sup{ EX,: t a stop rule} for Xl, X2,... independent uniformly bounded random variables; this yields results of Krengel,
A good life.
  • T. Hill
  • Medicine
    Social science & medicine
  • 1993
A Survey of Prophet Inequalities in Optimal Stopping Theory
This paper surveys the origin and development of what has come to be known as "prophet inequalities" in optimal stopping theory. Included is a review of all published work to date on these problems,
Fusions of a Probability Distribution
Starting with a Borel probability measure P on X (where X is a separable Banach space or a compact metrizable convex subset of a locally convex topological vector space), the class Y(P), called the
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