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

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:

    http://www.wolframalpha.com/input/?i=Integrate%5Be^%28t*x%29*%28k%2F%CE%BB%29*%28x%2F%CE%BB%29^%28k-1%29*e^-%28x%2F%CE%BB%29^k%2Cx%5D

    where the parameters are k and λ.

    The answer is found here:

    http://www.wolframalpha.com/input/?i=Sum%5B%28t^n+%CE%BB^n%29%2Fn%21%2C+{n%2C+0%2C+Infinity}%5D*gamma%281%2B%281%2Fk%29%29

    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

    User Avatar
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Deriving the MGF for the Weibull Distribution
Loading...