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st: -pweibull- and -qweibull- revised on SSC


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: -pweibull- and -qweibull- revised on SSC
Date   Tue, 4 Nov 2003 09:49:02 -0000

Thanks to Kit Baum, the packages -pweibull- and -qweibull- 
have been revised on SSC. These programs provide diagnostic plots 
for comparison of the distribution of a single 
variable with a two-parameter Weibull distribution. 

. ssc inst pweibull
. ssc inst qweibull 

will install in an up-to-date Stata with internet 
access. The option ", replace" will be necessary 
if you previously installed these packages. 

This follows my recent revision of -pexp- and -qexp-, 
announced on 31 October. 

In revising -pweibull- and -qweibull- from programs 
written in 1998, what was done was

0 To internalise the parameter estimation. 
(More on this below: a detail of interest 
way beyond this problem is the usefulness 
of -nlcom- for reparameterisation problems.) 

1 To revise the graphics to Stata 8. 

2 To support fweights and iweights. 

3 To allow generation of variables to hold
what was plotted. 

4 To allow fitting of the whole distribution, 
but a graph showing only part of the data, e.g. 
one tail. (This last arose out of a suggestion 
on a different problem by Stephen Jenkins.) 

In addition, these programs allow specification of 
parameter values (scale and shape parameters) as well 
as fitting the distribution on the fly. 

As implied, -pweibull- and -qweibull- now require Stata 8. 
The original versions, now renamed -pweibull4- and
-qweibull4-, remain in the package for any interested 
users of Stata 4 through 7. However, they are 
otherwise frozen as was and were not revised 
to incorporate 0 to 4 above. 

Nick 
n.j.cox@durham.ac.uk 

note on parameter estimation for Weibull distribution
=====================================================

To plot against what we would expect 
if the distribution were Weibull, we need parameter 
values, usually estimated from the data. 

The Stata solution that has been possible 
for some time is to set up the problem 
as one for the official Stata command -weibull-, 
which will yield maximum likelihood estimates. 
Note that no covariates are involved in this problem, 
nor are any required by -weibull-. A small difficulty 
then often ensuing is that the parameterisation 
used by -weibull- is chosen, it seems, for its suitability 
for survival modelling. At least one other
parameterisation is very common in the literature, 
even if, cosmetically, there is little agreement on the 
notation to be used. To convert from -weibull-'s 
parameterisation to this other one, a small wrapper 
program -wbull- is available on SSC, and it remains
a solution for users of Stata 5 through 7. 

As of Stata 8, 

* -weibull- has gone undocumented, and users 
are directed instead to -streg-. This strikes 
me as a small step backwards, as you can be 
interested in Weibull distributions without 
(consciously) engaging in survival (or reliability) analysis. 
To use -streg- you have to set up your problem as a survival 
problem even if it isn't. This is a very minor matter,
however, while -weibull- remains accessible. 

* -nlcom- offers a much better and more
general way of reparameterising the problem, 
for which many thanks. 

Anyway, -pweibull- and -qweibull- for Stata 8 now 
internalise parameter estimation. You 
don't need to estimate parameters separately. 
Conversely, you could even use -pweibull- 
or -qweibull- just as a way of estimating Weibull 
parameters, and ignore the graph, although naturally 
I wouldn't advise doing that. 

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