# Expectation of log(1/X) when X follows inverse gaussian distribution

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.

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