n p
> I want to simulate data (time to failure) from a
> Weibull distribution:
>
> p.d.f. :
> f(t)=lamda*gamma*t^(gamma-1)*exp(-lamda*t^gamma)
>
> (scale = lamda, shape=gamma)
>
> I have downloaded the "rnd" package (through "findit")
> and using the "rndwei" command I get the following
> puzzling (at least for me) results:
>
>
> . drop _all
>
> . rndwei 10000 1.5 0.0078
> ( Generating . )
> Variable xw created.
>
> . gen ev=1
>
> . stset xw ev
>
> failure event: ev ~= 0 & ev ~= .
> obs. time interval: (0, xw]
> exit on or before: failure
>
>
> . streg ,dist(wei) nohr nolog
>
> failure _d: ev
> analysis time _t: xw
> --------------------------
> _cons | -7.35076
> p | 1.513405
> --------------------------
>
> 1.513405 very close to 1.5
>
> but
>
> . di exp(-7.35076)
> .0006421
>
> and
>
> . di exp(-7.35076/1.513405)
> .00777299
>
> If I use the AFT form in streg, the exponentiated
> coefficient of the constant gives the correct result.
>
> I think this has to do with the parametrization used
> in "rndwei" but the help for this command is very
> limited. Do you think that rndwei is using some
> parametrization like lamda=(lamda')^gamma or am I
> missing something? I think that I have seen this
> parametrization among sociologists texts but my
> background is biostatistical (I was trying to
> replicate some examples from D. Collet's survival
> book)
>
> I would appreciate any other ideas for a Weibull
> simulation or even better a Weibull with frailties
> simulation.
When all else fails, look at the code.
For shape parameter gamma and scale parameter lambda, -rndwei-
boils down to one expression
((log(1/uniform()))^(1/ gamma)) / lambda
where naturally you need to plug in numbers instead
of parameter names.
That's got lambda as the reciprocal of the way
it is parameterised in two texts I looked at,
after which I stopped looking. As you say,
there are different parameterisations in
different literatures.
However, your own pdf looks wrong on
a casual glance, if only on dimensional grounds.
But for a two-parameter Weibull, random
number generation is just one line, and
you need not depend on anybody's program
once you know your own parameterisation.
Nick
[email protected]
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