There's a derivation for a special case of standard normal in Average norm of a N-dimensional vector given by a normal distribution
Is there a nice expression for the case of arbitrary diagonal covariance matrix?
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Squared norm yes, norm no. – kimchi lover Dec 11 '17 at 02:23
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This answer has a reference to it. – Dec 11 '17 at 04:43
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hm, I found the paper online here, but don't see the formula there – Yaroslav Bulatov Dec 11 '17 at 06:18
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The reference I meant was: "Multidimensional Gaussian Distributions" by Kenneth S. Miller (1964 edition, chapter 2, section 2) – Dec 15 '17 at 23:50
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I only got a copy of the book now, and was disappointed to find that where the author talks about "diagonal covariant matrix" (prior to Theorem 1 of Ch. 2 sec 2), he then proceeds to write a scalar multiple of identity. For general covariance there is some complicated symbolic expression with fractional derivatives in Theorem 7 of the same chapter; I don't know if it's of any practical use -- it's of the same kind as the last Theorem (page 909) of the Blumenson-Miller paper . Sorry. – Dec 19 '17 at 21:46
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https://math.stackexchange.com/questions/2723181/distribution-of-squared-euclidean-norm-of-gaussian-vector for squared norm – qwr Mar 28 '22 at 20:03