# How is the weibull distribution parameterised in survreg() in R [duplicate]

I was looking at how the weibull distribution is parameterised in survreg() in R and found a similar query posed in a thread at stack overflow: https://stackoverflow.com/questions/16236939/plot-survival-and-hazard-function-of-survreg-using-curve/51385718#51385718

The OPs query yielded 2 opinions:

1) scale=exp(intercept) 2) scale=exp(Intercept+beta*x)

If you go through ??survreg, you get this:

a) survreg's intercept = log(rweibull scale)

I also went through ??survreg.distributions and found this:

b) survreg scale parameter maps to 1/shape, linear predictor to log(scale)

b) obviously makes better sense - am I reading this right

To be more specific, I want to know how is the scale parameter from dweibull linked to the linear predictor from survreg(). I also consequently want to know how to compute the hazard function from the survreg() output.

• 1. See the help, which says "All the distributions are cast into a location-scale framework, based on chapter 2.2 of Kalbfleisch and Prentice. The resulting parameterization of the distributions is sometimes (e.g. gaussian) identical to the usual form found in statistics textbooks, but other times (e.g. Weibull) it is not. See the book for detailed formulas.". For the Weibull, explicit details are in the help on survreg. See also the first page here which explains the difference using the same information given in the help. ... ctd Jul 18, 2018 at 4:30
• ctd ... See also here and here and here and here (the ones relating to mean survival discuss the parameterization in the course of dealing with the mean). ... ctd Jul 18, 2018 at 4:33
• ctd... Failing all of that, simply simulating a few large sets of Weibull data and estimating the parameters in survreg is sufficient to figure out whats going on. Incompatible guesses can be quickly eliminated (well, all but one must be readily eliminated at least) Jul 18, 2018 at 4:41
• Thanks for the help - the links made it easier to understand a few of the things that I wasn't able to get a handle on and the advise on simulating a few large datasets and estimating the parameters in survreg was a gem. Jul 18, 2018 at 5:14
• I also found this helpful - a documentation from SAS and the way they parameterise the weibull survival model: support.sas.com/documentation/cdl/en/statug/63033/HTML/default/…. Here the SAS probability function PDF is similar to the dweibull in R Jul 18, 2018 at 7:00