Let $X$ follow non central chi distribution, the formula of $\mathbb{E}[\log(X)]$ (or equivalently $\mathbb{E}[\log(X^2)]$ where $X^2$ is Non central chi square) can be found here and here.

However, the formula contains polynominals that is complicated. I wonder if there is some approximation for this expectation.


  • $\begingroup$ Please post those sums in the body of your question. Also post your own attempts/thoughts. – Reviewer. $\endgroup$ – Jim May 20 '18 at 9:50
  • $\begingroup$ The first formula contains no infinite series: it's a polynomial. $\endgroup$ – whuber May 20 '18 at 16:32
  • $\begingroup$ @Jim My thought was that to calculate the expected value, I looked for the PDF and tried integrating it. That is what I wrote in the question. I don't see any other approachs. If it is obviously easy for you, what about give me some hints? $\endgroup$ – Cath Maillon May 21 '18 at 9:40
  • $\begingroup$ @whuber sorry, wrong words. $\endgroup$ – Cath Maillon May 21 '18 at 9:41
  • $\begingroup$ The distinction, though, is critical, isn't it? The polynomial is readily evaluated and not "complicated." This raises questions about what kind of "approximation" you seek and how well it should fit. Help out your readers by editing the question to address these issues specifically. $\endgroup$ – whuber May 21 '18 at 12:55

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