# Expectation with log normal

1. Oct 28, 2013

### 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

2. Oct 28, 2013

### 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 $\mathbb E [\log X]= E[Z] = \mu_Z$.

3. Oct 29, 2013

### econmath

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

Thanks.

4. Oct 29, 2013