# Re: [R] Quantile function for the generalized beta distribution of the 2nd kind

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Mon 12 Dec 2005 - 19:29:26 EST

Note that if you use integrate(), the result is not guaranteed to be smooth function of the parameters. I may well help to decrease the tolerances.

> but it doesn't work

Please see the posting guide, and tell us useful information about what precisely happened.

On Sun, 11 Dec 2005, Florent Bresson wrote:

> I have succeded in defining the cdf of the generalized
> beta of the second kind, eg.
>
> pgbeta2 <- function(quint,b,a,p1,p2) {
> integrate(function(x)
> {exp(log(a)+(a*p1-1)*log(x)-(a*p1)*log(b)-log(beta(p1,p2))-(p1+p2)*log(1+(x/b)^a))},0,quint)\$value
> }
>
> but I'm facing problems with the quantile function. I
> tried something like
>

> qgbeta2 <- function(proba,b,a,p1,p2) {
> optimize(function(z)
> {(proba-pgbeta2(z,b,a,p1,p2))^2},lower=0,
> upper=10^200) }
>
> but it doesn't work. I tried with other non linear
> optimization command like optim but it is apparently
> not the solution.
> Any idea ?
>
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>

```--
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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