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Refined Approximations for the Ewens Sampling Formula by A. D. Barbour is a Mathematics article available to read on EtoBox.
What is Refined Approximations for the Ewens Sampling Formula about?
## Abstract The Ewens sampling formula is a family of probability distributions over the space of cycle types of permutations of __n__ objects, indexed by a real parameter θ. In the case θ = 1, where the distribution reduces to that induced by the uniform distribution on all permutations, the joint distributions of the numbers of cycles of lengths less than __b = o(n)__ is extremely well approximated by a product of Poisson distributions, having mean 1/__j__ for cycle length __j__: the error is super‐exponentially small with __nb__^−1^. For θ ≠ 1. the analogous approximation, with means adjusted to θ/__j__, is good, but with error only linear in __n__^−1^__b__. In this article, it is shown that, by choosing the means of the Poisson distributions more carefully, an error quadratic in __n__^−1^__b__ can be achieved, and that essentially nothing better is possible.
Who reads Refined Approximations for the Ewens Sampling Formula?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- A. D. Barbour
- Publisher
- John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1042-9832)
- Published
- 1992
- Language
- EN
- ISBN
- 9783240030303
- Field
- Mathematics (Physical Sciences)