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

[Florent Bresson]

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 ?