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Gibbs Base Random Partitions Read chapter Read first chapter

2020 | OriginalPaper | Chapter

2. Asymptotic and Approximate Discrete Distributions for the Length of the Ewens Sampling Formula

Author : Hajime Yamato

Published in: Pioneering Works on Distribution Theory

Publisher: Springer Singapore

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Abstract

The Ewens sampling formula is well known as the probability for a partition of a positive integer. Here, we discuss the asymptotic and approximate discrete distributions of the length of the formula. We give a sufficient condition for the length to converge in distribution to the shifted Poisson distribution. This condition is proved using two methods: One is based on the sum of independent Bernoulli random variables, and the other is based on an expression of the length that is not the sum of independent random variables. As discrete approximations of the length, we give those based on the Poisson distribution and the binomial distribution. The results show that the first two moments of the approximation based on the binomial distribution are almost equal to those of the length. Two applications of this approximation are given.

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previous chapter Gibbs Base Random Partitions
next chapter Error Bounds for the Normal Approximation to the Length of a Ewens Partition
Appendix
Available only for authorised users
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Metadata
Title
Asymptotic and Approximate Discrete Distributions for the Length of the Ewens Sampling Formula
Author
Hajime Yamato
Copyright Year
2020
Publisher
Springer Singapore
Book
Pioneering Works on Distribution Theory

Print ISBN: 978-981-15-9662-9

Electronic ISBN: 978-981-15-9663-6

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-15-9663-6_2

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