I am recently working on fitting a model with incomplete beta function. In order to put it into my optimization algorithm, I must find out the derivatives of the incomplete beta function $B_p(x,y)$ and program it into computer.
I don't know how to do this, but I found a paper on Journal of Statistical Software:
Boik, Robert J., and James F. Robison-Cox. "Derivatives of the incomplete beta function." Journal of Statistical Software 3.1 (1998): 1-20.
The method on it is amazing and perform quite well and fast. I wonder if it is possible to use the same way to approximate any "sufficiently nice" (log-)likelihood function and its derivatives directly?
May I ask:
Any good reference book / survey paper on this topic?