[R] Weibull distribution

[Göran Broström]

On 7/21/06, Thomas Lumley <tlumley at u.washington.edu> wrote:
> On Fri, 21 Jul 2006, Valentin Dimitrov wrote:
>
> > Dear Leaf,
> >
> > I modified your code as follows:
> >
> > gamma.fun <- function(mu,sd,start=100)
> > {
> > f.fn <- function(alpha)
> > {abs(sd^2-mu^2/(gamma(1+1/alpha))^2*(gamma(1+2/alpha)-(gamma(1+1/alpha))^2))}
> > alpha <- optim(start, f.fn)
> > beta <- mu/gamma(1+1/alpha$par)
> > return(list=c(a=alpha$par,b=beta));
> > }
> >
> > Now it works properly.
> >
> > First, I added an abs(). You tried to solve an
> > equation by means of the R-function optim(), which
> > finds a minimum. That's why you can find the solution
> > of f(x)=a through minimization of abs(f(x)-a).
> > Second, I deleted the optim-method BFGS from the
> > optim() function, because it is not appropriate in
> > this case.
>
> optim() is not appropriate at all in this case -- its help page says to
> use optimize() for one-dimensional problems.

Just to clarify: The help page says:

'optim' will work with one-dimensional 'par's, but the default
method does not work well (and will warn).  Use 'optimize' instead.

In other words, if you for instance use the 'BFGS' method, optim is
perfectly OK for one-dimensional problems.
>
> In fact, in one dimension there isn't any need to resort to optimization
> when you really want root-finding, and uniroot() is more appropriate than
> optimize().

One reason to use optim instead of uniroot or optimize is that you
need not specify a finite interval that covers the solution.

Göran