Blanchet JH, Pacheco-González CG. UNIFORM CONVERGENCE TO A LAW CONTAINING GAUSSIAN AND CAUCHY DISTRIBUTIONS. Probability in the Engineering and Informational Sciences. 2012;26(3):437-448. doi:10.1017/S0269964812000101
Abstract
A source of light is placed d inches apart from the center of a detection bar of length L ≥ d. The source spins very rapidly, while shooting beams of light according to, say, a Poisson process with rate λ. The positions of the beams, relative to the center of the bar, are recorded for those beams that actually hit the bar. Which law best describes the time-average position of the beams that hit the bar given a fixed but long time horizon t? The answer is given in this paper by means of a uniform weak convergence result in L, d as t → ∞. Our approximating law includes as particular cases the Cauchy and Gaussian distributions.
Authors
Jose H Blanchet, Carlos G Pacheco-González
Publication date
2012/7
Journal
Probability in the Engineering and Informational Sciences
Volume
26
Issue
3
Pages
437-448
Publisher
Cambridge University Press
