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A Statistical Derivation of the Significant-Digit Law
- T. Hill
- Computer Science
- 1 November 1995
TLDR
Comparisons of Stop Rule and Supremum Expectations of I.I.D. Random Variables
- T. Hill, R. 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…
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…
Strong laws for L- and U-statistics
- J. 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,…
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,…
A Survey of Prophet Inequalities in Optimal Stopping Theory
- T. Hill, R. 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,…
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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