|Re: Cumulative Normal Distribution on HP Solve|
Message #3 Posted by Les Wright on 23 May 2006, 10:44 p.m.,
in response to message #2 by Les Wright
I now have Abramowitz and Stegun in front of me, and on closer inspection I can recommend the approximation of the inverse distribution, 26.2.23, with only modest enthusiasm. Absolute error quoted as less than 4.5e-4, which means the approximation is really only okay to 3 or at most 4 decimal places. I have run the code I referenced in the last post under P41CX, V41 and Free42, and, sure enough, the z-score associated with key alphas such as .01, .05, .001, etc matches more precise (? accurate) comparators such as UTPN in the HP48 series or the relevant computations in Maple up to about the fourth decimal place at best.
On the other hand, 26.2.17 in Abramowitz and Stegun claims absolute error less than 7.5e-8. If you could implement this approximation as the backbone of your equation in a Solver, then solve for the desired z for a given percentile or alpha (i.e., 1-percentile), you may get more decimal places, hopefully correct ones.
What exactly are you hoping for? Tell me more about program memory of the HP27.