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
>
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>
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