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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: estimating parameters of Weibull distribution |

Date |
Fri, 21 Feb 2003 21:02:00 -0000 |

Roberto G. Gutierrez, StataCorp. > > Clint Thompson <cthompson@dfpm.utah.edu> 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 n.j.cox@durham.ac.uk * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: estimating parameters of Weibull distribution***From:*rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp.)

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