What Is the Expectation E(log(x-a)) for a Log-Normally Distributed Variable x?

[econmath]

What is the expectation, E(log(x-a)), when x is log normally distributed? Also x-a>0. I am looking for analytical solution or good numerical approximation.

Thanks

 

[economicsnerd]

The random variable X is said to be log-normally distributed if \log X is normally distributed (I know, it's a weird naming convention). In other words, X= e^Z, where Z\sim \mathcal N(\mu_Z,\sigma_Z^2), a normal random variable. So then \mathbb E [\log X]= E[Z] = \mu_Z.

 

[econmath]

Yes of course, but I am looking for E[log (x-a)] not E[log(x)].

Thanks.

 

[economicsnerd]

Oh, yikes. I misread. Sorry for my useless answer.

I have no clue about your question.