Bernoulli Sieve

الأصل · EN

Bernoulli sieve is a recursive construction of a random composition (ordered partition) of integer n. This composition can be induced by sampling from a random discrete distribution which has frequencies equal to the sizes of component intervals of a stick-breaking interval partition of [0,1]. We exploit Markov property of the composition and its renewal representation to derive asymptotics of the moments and to prove a central limit theorem for the number of parts.