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?
This doesn't look pleasant at all:
http://en.wikipedia.org/wiki/Incomplete_gamma_function#Derivatives
It appears to be quite difficult to compute the derivative of the
incomplete gamma function itself -- I'm not aware of any R
implementation -- and the derivative of the inverse may be even harder.
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..
For all I know, the inverse is calculated by an (optimized) Newton-
type search algorithm, so it's not very likely that its derivative can
easily be worked out (based on the current implementation).
Best,
Stefan
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