Register to reply

Deriving the MGF for the Weibull Distribution

by donald17
Tags: deriving, distribution, weibull
Share this thread:
Apr12-11, 02:55 PM
P: 6
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:^%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:^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
Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Stephen Tashi
Apr12-11, 07:12 PM
Sci Advisor
P: 3,314
Those links you gave might be temporary URLs. I didn't get the first one to work.
Apr12-11, 08:16 PM
P: 6
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.

Register to reply

Related Discussions
Deriving equation of stored electrical energy in a charge distribution. Classical Physics 8
Deriving the binomial distribution formula Calculus & Beyond Homework 1
Lognormal shadowing + deriving pdf from normal distribution Electrical Engineering 0
Deriving cdf of ricean distribution + help Set Theory, Logic, Probability, Statistics 1
Modelling distribution and deriving probability of occurance being within a value Set Theory, Logic, Probability, Statistics 3