Stein's Method for Probability Distributions on 𝕊^1

05/27/2021

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by   Alexander Lewis, et al.

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In this paper, we propose a modification to the density approach to Stein's method for intervals for the unit circle 𝕊^1 which is motivated by the differing geometry of 𝕊^1 to Euclidean space. We provide an upper bound to the Wasserstein metric for circular distributions and exhibit a variety of different bounds between distributions; particularly, between the von-Mises and wrapped normal distributions, and the wrapped normal and wrapped Cauchy distributions.