Perfect simulation of Vervaat perpetuities
James Allen Fill, Mark Huber
TL;DR
This paper introduces a perfect simulation method for the Vervaat family of perpetuities, including the Dickman distribution, using coupling into and from the past for efficient sampling.
Contribution
It presents a novel coupling-based perfect sampling technique for Vervaat perpetuities, including the Dickman distribution, with proven efficiency.
Findings
Efficient perfect sampling algorithm developed
Applicable to the Dickman distribution in number theory and algorithms
Proven fast convergence of the sampling method
Abstract
We use coupling into and from the past to sample perfectly in a simple and provably fast fashion from the Vervaat family of perpetuities. The family includes the Dickman distribution, which arises both in number theory and in the analysis of the Quickselect algorithm, which was the motivation for our work.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Gaussian Processes and Bayesian Inference