Quantile function for the generalized beta distribution of the 2nd kind

The problem was with the use of the integrate command
for the definition of the cdf of the generalized beta
of the second kind. I solved the problem with a
transformation of the function qbeta. I then used an
optimize command but using uniroot is maybe  nicer. So
my function is :

qgbeta2  <-  function(proba,b,a,p1,p2) { val
<-qbeta(proba,p1,p2)   
                b*(uniroot(function(z) {z/(z+1)-val},
lower=0, upper=10000000,
tol=.Machine$double.eps^20)$root)^(1/a) }

The code is maybe not pretty but it works perfectly. I
just regret that it is not possible to fix the upper
limit of uniroot to Inf.

Thanks for help

--- Prof Brian Ripley <ripley at stats.ox.ac.uk> a ??crit
:

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 ?