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Can anybody help me in this question? How to derive the expectation of log(1/X) when X follows inverse Gaussian distribution?

Found out a type of approximation for $\mathbb{E}[\log(X)]$ while $X \sim \mathcal{N}(\mu,\sigma^2)$ in this link (Expected value and variance of log(a)). Can this be extended to the present case to get an approximate solution?

Any help will be appreciated.

Thanks in advance.

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  • $\begingroup$ How does such a question arise? Is this for a class, for your own study, or something else? $\endgroup$ – Glen_b♦ Jul 21 '15 at 0:16
  • $\begingroup$ This is coming in finding the lower bound for Variational Inference for a LASSO model. Can you help??? $\endgroup$ – Sandipan Karmakar Jul 21 '15 at 0:23
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    $\begingroup$ Okay, then how does the question of the lower bound for variational inference arise? Is this for a class, for your own study, or something else? $\endgroup$ – Glen_b♦ Jul 21 '15 at 0:25
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    $\begingroup$ It might be good to include that link (and your concerns about its applicability) in your question. $\endgroup$ – Glen_b♦ Jul 21 '15 at 0:41
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    $\begingroup$ $\log(1/X)=-\log(X)$, did you consider that? $\endgroup$ – mpiktas Jul 21 '15 at 7:33

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