Roberto G. Gutierrez, StataCorp.
>
> Clint Thompson <[email protected]> asks:
>
> > I need to estimate both parameters from the Weibull
> distribution (beta &
> > theta) using the maximum likelihood estimation method. I
> have referenced
> > the reference manual and it assumes that I am using a
> specific data set with
> > a Weibull distribution but I need the estimates using the
> general Weibull
> > pdf. I also want to estimate the variance-covariance
> matrix of the MLEs.
> > Any suggestions (aside from computing it by hand)?
>
> Very easy in Stata 8.
>
> Clint can fit a Weibull model without covariates on his
> univariate data and
> then use -nlcom- to remap the estimates to those from a
> more "typical" Weibull
> pdf. For example, if the pdf in question is
>
> f(t) = theta/beta * t^(theta-1) * exp(-t^theta/beta)
>
> and if one fits the Weibull model using the default
> proportional hazards (PH)
> parameterization, then the remapping would take place as follows:
>
> . webuse cancer
>
> . stset studytime /* studytime is the univariate response,
> no censoring */
>
> . streg, dist(weibull) nolog nohr
>
> (output omitted)
>
> . nlcom (theta:exp([ln_p]_b[_cons])) (beta:exp(-_b[_cons]))
>
> theta: exp([ln_p]_b[_cons])
> beta: exp(-_b[_cons])
>
> ------------------------------------------------------------
> ------------------
> _t | Coef. Std. Err. z P>|z|
> [95% Conf. Interval]
> -------------+----------------------------------------------
> ------------------
> theta | 1.518202 .1766894 8.59 0.000
> 1.171897 1.864506
> beta | 74.91051 42.54283 1.76 0.078
> -8.471904 158.2929
> ------------------------------------------------------------
> ------------------
>
> The estimated variance covariance matrix (VCE) of the
> remapping is returned
> in r(V).
>
> . mat list r(V)
>
> symmetric r(V)[2,2]
> theta beta
> theta .03121916
> beta 7.2700449 1809.8925
>
> As for a pre-Stata 8 solution, Clint would have to use
> -testnl- to obtain
> the derivative matrix and perform the delta method matrix
> calculations himself.
> A bit more prone to error, hence the motivation for -nlcom-.
>
As a footnote to Bobby's posting:
if you have not yet upgraded to Stata 8,
then -wbull- on SSC does some of this -- but
not the variance-covariance matrix you will want.
Blowing the dust off this ancient code, I see
that it requires Stata 5, so should work on 5, 6 and 7.
The graphics routines -qweibull- and -pweibull-
are of the same age and also are on SSC.
Nick
[email protected]
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