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"D. Mckenzie" <dmck@u.washington.edu< writes:
< Splus 2000 r3. < < I have fit a 2-parameter Weibull distribution to a data vector (fire-free < intervals in forests) and would like to compute the probability that the < shape parameter is greater than 1. I can use bootstrap() [I presume] to < compute the standard error. Is there a closed expression for CIs? (I < imagine a normal approximation would be pretty lame here). < < Thanks in advance for any suggestions. Profile likelihood would work well here. Because the conditional mle for the scale parameter, given the shape parameter, has a closed-form expression you can evaluate the profile log-likelihood for the shape parameter explicitly. I used this as an example in a presentation at the recent Joint Statistical Meetings on "Using Open Source Software to Teach Mathematical Statistics". (As you might guess from the title, I was primarily discussing another implementation of the S language but the examples work - with minor modifications - in S-PLUS.) The PDF file for the presentation is available as http://www.stat.wisc.edu/~bates/JSM2001.pdf Look especially at slide 26 where the profile log-likelihood function for the shape parameter is defined as < profilell <- function(alpha) + -sum(dweibull(xmp04.30$lifetime, shape = alpha, + scale = mean(xmp04.30$lifetimealpha)(1/alpha), log = TRUE)) < profilell(2.15) # negative profile log-likelihood at estimate [1] 77.0951 < mle3 <- nlm(profilell, c(alpha = 1.0), hessian = TRUE) < unlist(mle3[-3]) minimum estimate hessian code iterations 77.095088 2.152001 3.378437 1.000000 7.000000 (This is R, not S-PLUS. In S-PLUS I think you must evaluate dweibull without log = TRUE then take the log of the result and you would use ms rather than nlm.) Using the approximate distribution of twice the change in the profile log-likelihood as a chi-square with 1 df (at least I think that is the correct formula), you can construct confidence limits. --------------------------------------------------------------------- This message was distributed by s-news@lists.biostat.wustl.edu. To unsubscribe send e-mail to s-news-request@lists.biostat.wustl.edu with the BODY of the message: unsubscribe s-news
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