Complexity of Anticipated Rejection Algorithms and the Darling–Mandelbrot Distribution

We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the complexity is linear and admits as a limit law a so-called Darling–M...

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Bibliographic Details
Published inAlgorithmica Vol. 75; no. 4; pp. 812 - 831
Main Authors Bacher, Axel, Sportiello, Andrea
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2016
Subjects
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Theory of Computation
Sum of i.i.d. random variables
Random sampling
Anticipated rejection
Limit distribution
Darling–Mandelbrot distribution
Analysis of algorithms
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Summary:We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the complexity is linear and admits as a limit law a so-called Darling–Mandelbrot distribution, studied by Darling (Trans Am Math Soc 73:95–107, 1952 ) and Lew (Constr Approx 10(1):15–30, 1994 ). We also give an explicit form to the density of the Darling–Mandelbrot distribution and derive some of its analytic properties.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-015-0040-8