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Expectation with log normal

  1. Oct 28, 2013 #1
    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.

  2. jcsd
  3. Oct 28, 2013 #2
    The random variable [itex]X[/itex] is said to be log-normally distributed if [itex]\log X[/itex] is normally distributed (I know, it's a weird naming convention). In other words, [itex]X= e^Z[/itex], where [itex]Z\sim \mathcal N(\mu_Z,\sigma_Z^2)[/itex], a normal random variable. So then [itex]\mathbb E [\log X]= E[Z] = \mu_Z[/itex].
  4. Oct 29, 2013 #3
    Yes of course, but I am looking for E[log (x-a)] not E[log(x)].

  5. Oct 29, 2013 #4
    Oh, yikes. I misread. Sorry for my useless answer.

    I have no clue about your question.
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