Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
    /Hejdun
     
  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.

    /Hejdun
     
  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.

    Thanks.

    /Hejdun
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inverse of shifted lognormal
  1. Lognormal Distribution (Replies: 0)

  2. Lognormal distribution (Replies: 4)

Loading...