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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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  • $\begingroup$ Squared norm yes, norm no. $\endgroup$ – kimchi lover Dec 11 '17 at 2:23
  • $\begingroup$ This answer has a reference to it. $\endgroup$ – user357151 Dec 11 '17 at 4:43
  • $\begingroup$ hm, I found the paper online here, but don't see the formula there $\endgroup$ – Yaroslav Bulatov Dec 11 '17 at 6:18
  • $\begingroup$ The reference I meant was: "Multidimensional Gaussian Distributions" by Kenneth S. Miller (1964 edition, chapter 2, section 2) $\endgroup$ – user357151 Dec 15 '17 at 23:50
  • $\begingroup$ 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. $\endgroup$ – user357151 Dec 19 '17 at 21:46

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