Author: chandler yergin
Date: 16:02:37 04/26/05
Go up one level in this thread
On April 26, 2005 at 12:26:18, Eelco de Groot wrote: >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 Are you any relation to Adrian? Prof of applied Pysycology at Amsterdam U.? His book "Thought & Choice in Chess" was great!
This page took 0 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.