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Sep 19

Peter J Acklam inverse normal cumulative distribution

Posted by abiao at 13:23 | Code » Code site | Comments(0) | Reads(20108)
Random number generation is essential for Monte Carlo simulation, among random numbers, normal distributed numbers are undoubtedly the most widely used ones, here comes the problem, for a given uniform random numbers series, how do you compute the inverse normal cumulative distribution function?

I once introduced Moro inverse normal function for this purpose, here is another power function named Peter J Acklam inverse normal cumulative distribution, for my study and work i have tried both but couldnot decide which one is better, here i quote the sentence from the book "Monte carlo methos in finance" by Peter Jackel: Equally, for the inverse cumulative normal function z = N'(p), there are several numerical implementations providing different degrees of accuracy and efficiency. A very fast and accurate approximation is the one given by Boris Moro in [Mor95]. The most accurate whilst still highly efficient implementation currently freely available, however, is probably the algorithm by Peter Acklam. when allowing for an additional evaluation of a machine-accurate cumulative normal distribution function, Acklam’s procedure is able to produce the inverse cumulative normal function to full machine accuracy by applying a second stage refinement using Halley’s method.

Good, here is the page for Peter J Acklam inverse normal cumulative distribution codes in several languages, http://home.online.no/~pjacklam/notes/invnorm/index.html#The_algorithm, enjoy.

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