Hi William, Thanks a lot for your response. I checked the package and found that what I want to solve was the opposite, that is, from mean and sd to parameters shape and scale. Could anyone give some hints please? Any suggestion would be appreciated!
Leaf ----- Original Message ----- From: William Asquith, [EMAIL PROTECTED] Sent: 2006-07-17, 16:18:31 To: Leaf Sun, [EMAIL PROTECTED] Subject: Re: [R] Weibull distribution Do not have answer per se, but if you are seeking some comparisons-- try three parameter Weibull as implemented by the lmomco package. William On Jul 17, 2006, at 1:18 PM, Leaf Sun wrote: > Hi all, > > By its definition, the mean and variance of two-par. Weibull > distribution are: > > > > > > (www.wikipedia.org) > > > I was wondering, if given mean and sd. could we parameterize the > > distribution? I tried this in R. > > gamma.fun <- function(mu,sd,start=100) > { > f.fn <- function(alpha) sd^2-mu^2/(gamma(1+1/alpha))^2*(gamma(1+2/ > alpha)-(gamma(1+1/alpha))^2) > alpha <- optim(start, f.fn,method='BFGS') > beta <- mu/gamma(1+1/alpha$par) > return(list=c(a=alpha$par,b=beta)); > } > > > But the problems come up here: > > 1) the return values of a and b are only related to the input > > mean, and nothing to do with the sd. For instance, when I apply > a > mean mu = 3 whatever I use sd=2, sd=4, the function returned the > > same scale and shape values. > > > gamma.fun(3,4,10); > a b > 5.112554 3.263178 > > > gamma.fun(3,2,10); > a b > 5.112554 3.263178 > > 2) the start value determines the results: if I apply mean = 3, > and > sd=2, with a start of 10, it would return alpha close to 10, if > I > use a start = 100, it would return alpha close to 100. > > > gamma.fun(3,2,10); > a b > 5.112554 3.263178 > > > gamma.fun(3,2,100); > a b > 99.999971 3.017120 > > Since I am not a statistician, I guess there must be some > theoretical reasons wrong with this question. So I am looking > forward to some correction and advice to solve these. Thanks a > lot > in advance! > > Leaf > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting- > guide.html [[alternative HTML version deleted]] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.