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Math Help - MGF for the Rayleigh distribution

  1. #1
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    MGF for the Rayleigh distribution

    Hi, I'm trying to derive the moment generating function for the Rayleigh distribution.

    I know that it equals E(e^(t*x)), which is the following integral that can be seen here, evaluated at the limits of 0 and infinity:

    http://www.wolframalpha.com/input/?i...9%29%29%2Cx%5D

    Where the parameter is σ.

    However, I'm having trouble in the actual derivation of this. I've been trying to do a change of variable where u = -(x^2/(2*(sigma^2))), so that I can get the integral to appear somewhere for the error function, but I'm not making any progress. Can someone help me in moving this along? Thanks.
    Last edited by mr fantastic; April 12th 2011 at 03:44 PM. Reason: Corrected title, added tags to link.
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  2. #2
    MHF Contributor matheagle's Avatar
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    There doesn't seem to be a closed form for this MGF
    Rayleigh distribution - Wikipedia, the free encyclopedia
    I'm not sure what you need help with.
    Show me the calculations
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