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Math Help - How to obtain moment generating function for lognormal distribution.

  1. #1
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    How to obtain moment generating function for lognormal distribution.

    I can obtain
    <br />
M_{X}(t) = e^{\mu t + \sigma^{2}t^{2}/2}<br />
    as the moment generating function of the normal distribution but I dont see the step to obtain
    <br />
E(X^n) = e^{n \mu + \frac{1}{2}n^{2}\sigma^{2}}<br />
    as the Taylor series elements of the lognormal moment generating function.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Since Y=\ln X we have e^Y=X.

    So, MGF_Y(t)=E(e^{Yt})=E(X^t) using  e^{Yt}=(e^Y)^t=X^t.

    Or MGF_Y(n)=E(X^n).
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