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- Theodore P. Hill
- 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… (More)

- Theodore P. Hill
- 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… (More)

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… (More)

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,… (More)

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,… (More)

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… (More)

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… (More)

- Theodore P. Hill
- 1987

On cherche a determiner des bornes de partition les meilleures possibles comme fonction de la taille maximum des atomes

- Theodore P. Hill
- 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,… (More)

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.… (More)