The Bernoulli Sieve

The Bernoulli Sieve

The Bernoulli sieve is a recursive construction of a random composition (ordered partition) of an integer n. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of components of a stick-breaking interval partition of [0, 1]. We exp...

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Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2004-02, Vol.10 (1), p.79-96
1. Verfasser: Gnedin, Alexander V.
Format: Artikel
Sprache:eng
Schlagworte:
Central limit theorem
composition
Harmonic functions
Integers
Logarithms
Markov chains
Mathematical moments
Polynomials
Property composition
Recursion
renewal
sampling
stick-breaking
Written composition
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Beschreibung
Zusammenfassung:The Bernoulli sieve is a recursive construction of a random composition (ordered partition) of an integer n. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of components of a stick-breaking interval partition of [0, 1]. We exploit the Markov property of the composition and its renewal representation to study the number of its parts. We derive asymptotics of the moments and prove a central limit theorem.
ISSN:1350-7265
DOI:10.3150/bj/1077544604