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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