From: Leaf Sun <leaflovesun_at_yahoo.ca>

Date: Fri 21 Jul 2006 - 01:57:08 EST

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. Received on Fri Jul 21 02:07:40 2006

Date: Fri 21 Jul 2006 - 01:57:08 EST

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, wasquith@austin.rr.com
Sent: 2006-07-17, 16:18:31

To: Leaf Sun, leaflovesun@yahoo.ca

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]]
**>
**> ______________________________________________
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**> PLEASE do read the posting guide! http://www.R-project.org/posting-
**> guide.html
*

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