Author: Eelco de Groot
Date: 09:26:18 04/26/05
Go up one level in this thread
On April 25, 2005 at 16:05:59, Dieter Buerssner wrote: >Odd Gunnar, sorry for the slow response. Perhaps there is a small >misunderstanding. I feel, that it is not best to use this approximation formula >nowadays. Transcendental functions (like erf, log, pow) are easily and with very >high accuracy available nowadays. No need to use the approximation. Even, when >you cannot inverse (like it seems to be the case for erf(), which is needed when >using the normal distribution - with the logistic distribution inversion is >easy), one can easily do it with numerical methods and the "real" formula. IIRC >more sophisticated math libraries (like Steven Moshier's cephes, that is freely >available in source) can even inverse erf() with very high accurracy, very good >perfomance, and just a function call. Of course the differences will only show >in the tails (large Elo difference) and are rather theoretical. In these tails, >the assumptions made are most probably not true anymore anyway - so it is a >rather theoretical argument. > >Remi has done a model based on Bayesian statistics, which seems to make less >assumptions (I don't understand it fully). Martin Glickman (the inventor of the >Glicko rating system used on chess servers) seems to use Bayesian statistics in >his newest publications, as well. > >Regards, >Dieter Dieter, Odd Gunnar, I just wanted to add that for most elo purposes Hasting's approximation seems good enough to get the area under the Gaussian distribution, the absolute error of this approximation is about 7,5 x10^-8 as I found mentioned on the web. If you have code for the error function, please bear in mind I think it is slightly different than the Phi() function as I used it: Phi(x) = ½ + ½ erf(x/(2^0.5)) http://mathworld.wolfram.com/NormalDistributionFunction.html An good approximation for the error function can also be found in Numerical Recipes. Otherwise, to integrate erf() numerically you can use for instance Newton's method again like in Rtdiff() Eelco
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.