Articles
Criticisms of the proposed “new SI”, Accreditation and Quality Assurance: Journal for Quality, Comparability, and Reliability in Chemical Measurement (2011)
A Stronger Conclusion to the Classical Ham Sandwich Theorem (with John H. Elton), European Journal of Combinatorics (2011)
The conclusion of the classical ham sandwich theorem for bounded Borel sets may be strengthened,...
Finite-state Markov Chains Obey Benford’s Law (with Arno Berger, Bahar Kaynar, and Ad Ridder), SIAM Journal on Matrix Analysis and Applications (2011)
A sequence of real numbers (xn) is Benford if the significands, i.e., the fraction parts...
Conflations of Probability Distributions, Transactions of the American Mathematical Society (2011)
The conflation of a finite number of probability distributions P1,...,Pn is a consolidation of those...
Benford’s Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem (with Arno Berger), The Mathematical Intelligencer (2011)
Towards a Better Definition of the Kilogram (with Jack Miller and Albert C. Censullo), Metrologia (2011)
It is widely accepted that improvement of the current International System of Units (SI) is...
A Basic Theory of Benford’s Law (with Arno Berger), Probability Surveys (2011)
Drawing from a large, diverse body of work, this survey presents a comprehensive and unified...
Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law (with Arno Berger), Mathematics ArXiv (2010)
Feller’s classic text An Introduction to Probability Theory and its Applications contains a derivation of...
Obituary for Lester Eli Dubins, 1921-2010 (with David Gilat and Bill Sudderth), Bernoulli News (2010)
Finite-state Markov Chains Obey Benford’s Law (with Babar Kaynar, Arno Berger, and Ad Ridder), Mathematics arXiv (2010)
A sequence of real numbers (xn) is Benford if the significands, i.e. the fraction parts...
An Optimal Method to Combine Results from Different Experiments (with Jack Miller), Physics arXiv (2009)
Counterexamples in the Theory of Fair Division (with Kent E. Morrison), Mathematics arXiv (2009)
Ham Sandwich with Mayo: A Stronger Conclusion to the Classical Ham Sandwich Theorem (with John H. Elton), Mathematics arXiv (2009)
The conclusion of the classical ham sandwich theorem of Banach and Steinhaus may be strengthened:...
Conflations of Probability Distributions, Mathematics arXiv (2008)
The conflation of a finite number of probability distributions P1,..., Pn is a consolidation of...
Scale-Distortion Inequalities for Mantissas of Finite Data Sets (with Arno Berger and Kent E. Morrison), Journal of Theoretical Probability (2008)
In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to...
A Better Definition of the Kilogram (with Ronald F. Fox), Physics arXiv (2007)
Fixing the value of Avogadro's constant, the number of atoms in 12 grams of carbon-12,...
A characterisation of Newton maps (with Arno Berger), Australian & New Zealand Industrial and Applied Mathematics Journal (2006)
Conditions are given for a Ck map T to be a Newton map, that is,...
Regularity of digits and significant digits of random variables (with Klaus Schürger), Stochastic Processes and their Applications (2005)
A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of...
One-Dimensional Dynamical Systems and Benford's Law (with Arno Berger and Leonid A. Bunimovich), Transactions of the American Mathematical Society (2005)
Near a stable fixed point at 0 or ∞, many real-valued dynamical systems follow Benford's...
Constructing Random Probability Distributions (with David E.R. Sitton), Abstract and Applied Analysis (2004)
This article surveys several classes of iterative methods for constructing random probability distributions (or random...
Maximin Share and Minimax Envy in Fair-Division Problems (with Marco Dall'Aglio), Journal of Mathematical Analysis and Applications (2003)
For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the...
Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes Transform (with Jeffrey S. Geronimo), Journal of Approximation Theory (2003)
The pointwise limit S of a sequence of Stieltjes transforms (Sn) of real Borel probability...
Levy-like Continuity Theorems for Convergence in Distribution (with Ulrich Krengel), Proceedings of the Gottingen Academy of Sciences (2002)
Levy’s classical continuity theorem states that if the pointwise limit of a sequence of characteristic...
Random Probability Measures with Given Mean and Variance Running title: Random Probability Measures (with Lisa Bloomer), Journal of Theoretical Probability (2002)
This article describes several natural methods of constructing random probability measures with prescribed mean and...
Extreme-Value Moment Goodness-of-Fit Tests (with Victor Perez-Abreu), Annals of Institute of Statistical Mathematics (2001)
A general goodness-of-fit test for scale-parameter families of distributions is introduced, which is based on...
Alternative Empirical Distributions Based on Weigted Linear Combinations of Order Statistics (with James Mann), Stochastic Analysis and Applications (2000)
A class of empirical distributions is introduced which are based on various weighted linear combinations...
Goal Problems in Gambling Theory, Revista de Matemática: Teoria y Aolicaciones (1999)
A short introduction to goal problems in abstract gambling theory is given, along with statements...
On the Basic Representation Theorem for Convex Domination of Measures (with J. Elton), Journal of Mathematical Analysis and Applications (1998)
A direct, constructive proof is given for the basic representation theorem for convex domination of...
Constructions of Random Distributions via Sequential Barycenters (with Michael Monticino), The Annals of Statistics (1998)
This article introduces and develops a constructive method for generating random probability measures with a...
A Note on Distributions of True Versus Fabricated Data, Perceptual and Motor Skills (1996)
New empirical evidence and statistical derivations of Benford’s Law have led to successful goodness-of fit...
Strongly-Consistent, Distribution-Free Confidence Intervals for Quantiles (with David Gilat), Statistics and Probability Letters (1996)
Strongly-consistent, distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown...
Strong Laws for L- and U-Statistics (with J. Aaronson, R. Burton, H. Dehling, D. Gilat, and B. Weiss), Transactions of the American Mathematical Society (1996)
Strong laws of large numbers are given for L-statistics (linear combinations of order statistics) and...
A Statistical Derivation of the Significant-Digit Law, Statistical Science (1995)
The history, empirical evidence and classical explanations of the significant-digit (or Benford's) law are reviewed,...
Base-Invariance Implies Benford's Law, Proceedings of the American Mathematical Society (1995)
A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of...
On the Relationship Between Convergence in Distribution and Convergence of Expected Extremes (with M. C. Spruill), Proceedings of the American Mathematical Society (1994)
It is well known that the expected values {Mk(X)}, k ≤ 1, of the k-maximal...
Minimax-Optimal Strategies for the Best-Choice Problem When a Bound is Known for the Expected Number of Objects (with D. P. Kennedy), SIAM Journal of Control and Optimization (1994)
For the best-choice (or secretary) problem with an unknown number N of objects, minimax-optimal strategies...
Quantile-Locating Functions and the Distance Between the Mean and Quantiles (with D. Gilat), Statistica Neerlandica (1993)
Given a random variable X with finite mean, for each 0 < p < 1,...
Partitioning Inequalities in Probability and Statistics, Stochastic Inequalitites (1993)
This article surveys fair-division or cake-cutting inequalities in probability statistics, including bisection inequalities, basic fairness...
Moment-Based Minimax Stopping Functions for Sequences of Random Variables (with Frans A. Boshuizen), Stochastic Processes and Their Applications (1992)
Minimax-optimal stopping times and minimax (worst-case) distributions are found for the problem of stopping a...
On the Game of Googol (with Ulrich Krengel), International Journal of Game Theory (1992)
In the classical secretary problem the decision maker can only observe the relative ranks of...
Sharp Inequalities for Optimal Stopping with Rewards Based on Ranks (with D. P. Kennedy), The Annals of Applied Probability (1992)
A universal bound for the maximal expected reward is obtained for stopping a sequence of...
On the Construction of Generalized Measure Preserving Transformations With Given Marginals (with Ulrich Krengel), Lecture Notes in Mathematics (1992)
Measure preserving transformations generate stationary processes and vice versa. Which processes (X i ) correspond...
A Prophet Inequality Related to the Secretary Problem (with Ulrich Krengel), Contemporary Mathematics (1992)
Let Z1, Z2 , .. . , Zn be independent 0-1-valued random variables. A gambler...
A Survey of Prophet Inequalities in Optimal Stopping Theory (with Robert P. Kertz), Contemporary Mathematics (1992)
This paper surveys the origin and development of what has come to be known as...
Fusions of a Probability Distribution (with J. Elton), The Annals of Probability (1992)
Starting with a Borel probability measure P on X (where X is a separable Banach...
One-Sided Refinements of the Strong Law of Large Numbers and the Glivenko-Cantelli Theorem (with David Gilat), The Annals of Probability (1992)
A one-sided refinement of the strong law of large numbers is found for which the...
Minimax-Optimal Stop Rules and Distributions in Secretary Problems (with Ulrich Krengel), The Annals of Probability (1991)
For the secretary (or best-choice) problem with an unknown number N of objects, minimax-optimal stop...
A Generalization of Levy's Concentration-Variance Inequality (with R. D. Foley and M. C. Spruill), Probability Theory and Related Fields (1990)
Sharp lower bounds are found for the concentration of a probability distribution as a function...
Prophet Inequalities for Parallel Processes (with D. P. Kennedy), Journal of Multivariate Analysis (1989)
Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel...
Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing (with Y. L. Tong), The Annals of Probability (1989)
Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best...
Equitable Distribution of Indivisible Objects (with Stephen Demko), Mathematical Social Sciences (1988)
Deterministic and randomized solutions are developed for the problem of equitably distributing m indivisible indivisible...
A Proportionality Principle for Partitioning Problems, Proceedings of the American Mathematical Society (1988)
In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the...
A Sharp Partitioning-Inequality for Non-Atomic Probability Measures Based on the Mass of the Infimum of the Measures, Probability Theory and Related Fields (1987)
If μ1, ... ,μn are non-atomic probability measures on the same measurable space (S, F),...
Partitioning General Probability Measures, The Annals of Probability (1987)
Suppose μ1, ..., μn are probability measures on the same measurable space (Ω, F). Then...
A Generalization of Lyapounov's Convexity Theorem to Measures with Atoms (with John Elton), Proceedings of the American Mathematical Society (1987)
The distance from the convex hull of the range of an n-dimensional vector-valued measure to...
The Existence of Good Markov Strategies for Decision Processes with General Payoffs (with Victor C. Prestien), Stochastic Processes and their Applications (1987)
For countable-state decision processes (dynamic programming problems), a general class of objective functions is identified...
Expectation Inequalities Associated With Prophet Problems, Stochastic Analysis and Applications (1987)
Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of...
Prophet Inequalities for Averages of Independent Non-Negative Random Variables, Mathematische Zeitschrift (1986)
Optimal-Partitioning Inequalities for Nonatomic Probability Measures (with John Elton and Robert P. Kertz), Transactions of the American Mathematical Society (1986)
Suppose μ1,...,μn are nonatomic probability measures on the same measurable space (S, B). Then there...
On Maximizing the Average Time at a Goal (with S. Demko), Stochastic Processes and Their Applications (1984)
In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary...
Almost Sure Stability of Partial Sums of Uniformly Bounded Random Variables, Proceedings of the American Mathematical Society (1983)
Suppose a1 , a2 ,... is a sequence of real numbers with an → ∞....
Determining a Fair Border, The American Mathematical Monthly (1983)
In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the...
Stop Rule Inequalities for Uniformly Bounded Sequences of Random Variables (with Robert P. Kertz), Transactions of the American Mathematical Society (1983)
If X0, X1, ... is an arbitrarily-dependent sequence of random variables taking values in [0,1]...
The Advantage of Using Non-Measurable Stop Rules (with Victor C. Prestien), The Annals of Probability (1983)
Comparisons are made between the expected returns using measurable and non-measurable stop rules in discrete-time...
Conditional Generalizations of Strong Laws Which Conclude the Partial Sums Converge Almost Surely, The Annals of Probability (1982)
Suppose that for every independent sequence of random variables satisfying some hypothesis condition H, it...
Comparisons of Stop Rule and Supremum Expectations of I.I.D. Random Variables (with Robert P. Kertz), The Annals of Probability (1982)
Implicitly defined (and easily approximated) universal constants 1.1 < an < 1.6, n = 2,3,...
Additive Comparisons of Stop Rule and Supremum Expectations of Uniformly Bounded Independent Random Variables (with Robert P. Kertz), Proceedings of the American Mathematical Society (1981)
Let XI, X2, . . . be independent random variables taking values in [a, b],...
Ratio Comparisons of Supremum and Stop Rule Expectations (with Robert P. Kertz), Probability Theory and Related Fields (1981)
Suppose X1,X2,...,Xn are independent non-negative random variables with finite positive expectations. Let Tn denote the...
Decision Processes with Total-Cost Criteria (with Steven Demko), The Annals of Probability (1981)
By a decision process is meant a pair (X,Γ), where X is an arbitrary set...
On the Existence of Good Markov Strategies, Transactions of the American Mathematical Society (1979)
In contrast to the known fact that there are gambling problems based on a finite...