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- Publications
- Influence
A Statistical Derivation of the Significant-Digit Law
- T. Hill
- Mathematics
- 1 November 1995
The history, empirical evidence and classical explanations of the significant-digit (or Benford's) law are reviewed, followed by a sum- mary of recent invariant-measure characterizations. Then a new… Expand
Base-Invariance Implies Benford's Law
- T. Hill
- Mathematics
- 1 March 1995
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… Expand
Comparisons of Stop Rule and Supremum Expectations of I.I.D. Random Variables
- T. Hill, Robert P. Kertz
- Mathematics
- 1 May 1982
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… Expand
Strong laws for L- and U-statistics
- Jon Aaronson, R. Burton, H. Dehling, D. Gilat, T. Hill, B. Weiss
- Mathematics
- 1 July 1996
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,… Expand
Prophet inequalities and order selection in optimal stopping problems
- T. Hill
- Mathematics
- 1983
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,… Expand
A Survey of Prophet Inequalities in Optimal Stopping Theory
- T. Hill, Robert P. Kertz
- Mathematics
- 1992
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,… Expand
Partitioning General Probability Measures
- T. Hill
- Mathematics
- 1 April 1987
On cherche a determiner des bornes de partition les meilleures possibles comme fonction de la taille maximum des atomes
Stop rule inequalities for uniformly bounded sequences of random variables
- T. Hill, Robert P. Kertz
- Mathematics
- 1983
If X0, XI..._ is an arbitrarily-dependent sequence of random variables taking values in [0, I] and if V( XA0, X,. . .) is the supremum, over stop rules t, of EX,, then the set of ordered pairs {(x,… Expand
Additive Comparisons of Stop Rule and Supremum Expectations of Uniformly Bounded Independent Random Variables
- T. Hill, Robert P. Kertz
- Mathematics
- 1 March 1981
Let XI, X2, . . . be independent random variables taking values in [a, b], and let T denote the stop rules for X1, X2, Then E(sup,, X,,) sup{EX,: t E T) < (1/4)(b a), and this bound is best possible.… Expand
A basic theory of Benford's Law ∗
Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits… Expand