Paul A Bristow wrote:
A brief study of this (kindly provided by Oliver Seiler) shows it to be 'interesting' - but outstandingly accurate.
MathCAD appears to offer the density, cumulative and inverse, so this could provide some independent test values.
K Krishnamoorthy, Handbook of Statistical distributions with applications, in Chapter 4 deals with this distribution and also gives FORTRAN algorithms, but Wu (see above ref) shows that these approximations can be spectacularly inaccurate at times.
So this (and other distributions) might be a good GSoC?
I don't think it's big enough for a SOC on it's own - shouldn't be more than a couple of days work - a week at worst? The tricky bit as Wu notes is calculating the h(0) term - after that it's a reasonably straightforward series evaluation. But... I'm not completely convinced by the practicality of Wu's method - it's really very cunning, no doubt about that - but requires a table of all the prime numbers smaller than the sample size, the first 1000 primes would take you up to 8K, but then you need another table of the same size to keep track of all the common factors (unless I'm missing a trick somewhere). We could get the first term from two calls to tgamma_delta_ratio, but I haven't completely convinced myself that it won't unnecessarily under/overflow. Otherwise you're into using logs and lgamma, which is rather prone to cancellation errors in calculating the result :-( John.