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On the sum of t and Gaussian random variables

By Guy P. Nason

Abstract

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student's t-distribution on odd degrees of freedom greater than or equal to three. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calculations in the theoretical analysis of projection indices and computation of certain moments.Sum of Gaussian and Student's t Characteristic function Wavelet shrinkage Error function

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