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Thread: Complex integration of a moment generating function

  1. #1
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    Complex integration of a moment generating function

    Hi,
    I have a moment generating function (infinite series). Supposedly, I can recover the probability distribution by doing the following integration:
    f(x) = int m(t)exp(-tx) dt /(2ipi),
    the integration going from c-i*infinity to c+i*infinity.


    As an example, the moment generating function for a gaussian is exp(mu*t+sigma^2*t^2*1/2). Can someone show me how to do this integration? Especially if the mgf is expanded in a taylor series...THANKS!
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  2. #2
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    Quote Originally Posted by langweilig View Post
    Hi,
    I have a moment generating function (infinite series). Supposedly, I can recover the probability distribution by doing the following integration:
    f(x) = int m(t)exp(-tx) dt /(2ipi),
    the integration going from c-i*infinity to c+i*infinity.


    As an example, the moment generating function for a gaussian is exp(mu*t+sigma^2*t^2*1/2). Can someone show me how to do this integration? Especially if the mgf is expanded in a taylor series...THANKS!
    There's a connection between the moment generating function and the Laplace transform. I have no time to elaborate now. You might have a read of this: http://www.bibalex.org/Supercourse/S...0001/19461.pdf
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