Hi!
I know the relationship between the Weibull and the Gumbel, i.e. if T is
Weib than log-e (T) is Gumbel.
Also, I understand how to prove that. however, I fail to prove how the
Gumbel evolves from the 3-parameter Weibull. So far, I have the following:
R: Reliability function
R_sub_Y(y)=P(Y>y)=P(logT>y)=P(T>exp(y))=R_sub_T(exp(y))
=exp(-(exp(y)/alpha)^beta)=exp(-exp((y-gamma)/eta))
with eta=1/beta and
gamma=log alpha
If I try to do the same with the three-parameter Weibull, then
R_sub_T(exp(y))=exp(-((exp(y)-delta)/alpha)^beta)
where delta=location parameter for the Weibull distribution.
Any idea/hep available?
Thanks a lot! Ulrich
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