

Dear all,

I would be very grateful if you could help me with:

Given the regularized gamma function Reg=int_0^r (x^(k-1)e^(-x))dx/int_0^Inf (x^(k-1)e^(-x))dx ; 0<r<Inf (which is eventually the ratio of the
Incomplete gamma function by the gamma function), does anyone know of a package in R that would evaluate the derivative of the inverse of Reg with respect to k? I am aware that the function "Rgamma.inv" of the package "Zipfr" evaluates the inverse
of Reg and I'm wondering wether there is a function that would evaluate the derivative of the inverse..

Alternatively, a good numerical integration package/ or simply a function that could evaluate the integral int_0^r (log(x) x^(k-1) e^(-x))dx;  0<r<Inf
would be useful. I tried the function "int" of the package "rmutil" but I'm not sure wether it is accurate especially for small values of k. Does R have a powerful numerical integration package that can deal with such functions especially when the limit close to zero in + or - Inf?

Many thanks for this opportunity to post our queries,

Amy



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