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Inverse of shifted lognormal

  1. Nov 20, 2011 #1
    Hi everyone,

    I am stuck with this problem. I am looking for E(1/(1 + e^Z)) where Z is a normally distributed random variable.

    I know that E(e^Z) and E(1/e^Z) follow lognormal and inverse lognormal distibution and the means of these distributions are standard results. Of course, is also easy to find E(e^Z + 1).

    However regarding my problem, does anyone have a suggestion of how to proceed? I tried to use the moment generating function but got stuck...

    Thanks in advance!
  2. jcsd
  3. Nov 22, 2011 #2
    Sorry to bump this.

    Still no ideas of how to solve this problem?

    Of course, I can approximate it using Taylor expansion, but the
    resulting expression isn't very nice.

  4. Nov 22, 2011 #3
    Maybe Gauss-Hermite quadrature will give you a decent approximation?
  5. Nov 22, 2011 #4
    Yes, the integral may be evaluated numerically,
    but I am looking for an analytical answer. I am not sure how the Gauss-Hermite quadrature would help for such a case.


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