2015 review of icdf approximations with bad links
benchmark ziggurat2000 > MontyPython1998 > PPND71988(wichura) > Polar1969
William shaw 2007 (n,d) numerator and denominator degree (3,4) Beasley-Springer-Moro (BSM) ==> modified, fastest (-24.820209533706798850 y3 + 40.864622120467790785 y2 - 18.515898959450185753 y + 2.5066282682076065359) / (3.0154847661978822127 y4 - 20.641301545177201274 y3 + 22.831834928541562628 y2 - 8.4339736056039657294 y + 1) => relative error < 2.6E-9 in central BSM region (7,7) Wichura "AS241" (1988) => modified, most accurate => machine precision (5,5) Acklam algorithms
polynomial only: 1, 7/6, 127/90, 4369/2520, 34807/16200, 20036983/7484400, 2280356863/681080400 (7) relative < 1E-9 in a region extending to about u = 0.64to 0.7 ==> cdf(r=x-1/2) = r + 7/6r2 + 127/90r3 ...
2016 THOMAS LUU FAST AND ACCURATE PARALLEL COMPUTATION OF QUANTILE FUNCTIONS FOR RANDOM NUMBER GENERATION
- Modern simulation methods such as quasi-Monte Carlo and copula methods call for direct inversion of CDFs breakpoints b = 0.08 for Moro [55], • b = 0.075 for Wichura (Algorithm AS 241) [83], • b = 0.02425 for Acklam [2].