R help - Dec 2005 - Quantile function for the generalized beta distribution of the 2nd kind

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 ?

Don't you want to use uniroot() to find quantiles?  It is the usual way.

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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> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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