Local limit theorems and probability metrics bounds for the inverse Gaussian distribution and its multivariate extension

09/10/2022

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by   Frédéric Ouimet, et al.

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In this paper, we prove a local limit theorem and probability metrics bounds between the inverse Gaussian distribution (also called the Wald distribution) and the normal distribution with the same mean and variance. We also extend these results to the multivariate inverse Gaussian distribution introduced by Minami (2003).