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Deriving the MGF for the Weibull Distribution

  1. Apr 12, 2011 #1
    I'm attempting to derive the MGF for the Weibull distribution. I know that E([tex]e^{tx}[/tex]), which equals the integral shown here:


    where the parameters are k and λ.

    The answer is found here:


    So I see that I need to get the gamma function and the series representation for e^(t*λ) to show up in order to get the right answer. I've been trying to use a change of variable such as u = (x/λ)^k, and I feel like I've been getting close, but can't exactly get it right. Can someone guide me along with this? Thank you.

    *For some reason it keeps putting a space in the URL, so just take them out
  2. jcsd
  3. Apr 12, 2011 #2

    Stephen Tashi

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    Science Advisor

    Those links you gave might be temporary URLs. I didn't get the first one to work.
  4. Apr 12, 2011 #3
    In the first url try copy and pasting the whole thing, but taking out the space between the 2 and the F

    Similarly, for the second url take out the space between the I and the nfinity. If this doesn't work let me know and I'll attempt to repost what I'm trying to show in another format.
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