82 citations · 199 across the 24 of their papers we have counts for
6 papers · 1 filter
Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models
Jay Bartroff, Larry Goldstein, Ümit Işlak
Threshold-type counts based on multivariate occupancy models with log concave marginals admit bounded size biased couplings under weak conditions, leading to new concentration of m…
A Berry-Esseen bound for the uniform multinomial occupancy model
Jay Bartroff, Larry Goldstein
The inductive size bias coupling technique and Stein's method yield a Berry-Esseen theorem for the number of urns having occupancy when balls are uniformly distribute…
The Fighter Problem: Optimal Allocation of a Discrete Commodity
Jay Bartroff, Ester Samuel-Cahn
The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which f…
A Proof of the Bomber Problem's Spend-It-All Conjecture
Jay Bartroff
The Bomber Problem concerns optimal sequential allocation of partially effective ammunition while under attack from enemies arriving according to a Poisson process over a time…
On Optimal Allocation of a Continuous Resource Using an Iterative Approach and Total Positivity
Jay Bartroff, Larry Goldstein, Yosef Rinott +1
We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount~…
The Spend-It-All Region and Small Time Results for the Continuous Bomber Problem
Jay Bartroff, Larry Goldstein, Ester Samuel-Cahn
A problem of optimally allocating partially effective ammunition to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time~$t…