Author: Rémi Coulom
Date: 06:10:59 12/23/02
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On December 23, 2002 at 06:31:57, Peter Fendrich wrote: > >Remi, >I don't get the same results as you: >(all the sample values of Pw, Pd, Trin and cumTrin are the same) > Mine Yours >4 6 0 : 0.2745363 0.2745533 >4 6 1 : 0.274543 0.2747703 >4 6 10: 0.2740947 0.2773552 > >I'm not sure what's happening here but as you say, the Monte Carlo method >doesn't give exact values. >I thought that the program could be reliable to 3 decimals but maybe not... >However, if I'm right about draws, the prob would slowly move towards 0.5 when >the number of draws increases. I continued up to 500 draws and got the >following: >4 6 100: 0.2758096 >4 6 200: 0.2820387 >4 6 300: 0.2906555 >4 6 400: 0.3076096 >4 6 500: 0.3273436 That is because the Monte Carlo method is inaccurate: think about the x^n function, x varying between 0 and 1: when n grows large, the function has an extremely thin peak, that is very difficult to integrate accurately with a Monte Carlo method. I am totally certain about this, because I first started by implementing a program that calculated the big trinomial integrals. I wrote a small polynom library based on the GNU multiprecision library so that the _exact_ value was found. That's how I noticed that the result does not depend on draws, and went further in the calculations. > >The probability for A neatly grows with more draws. >OTOH I can't argue against your formulas. Give me some more time. >Could you please elaborate the first formula in section "3 Draws do nout Count". >How do explain 1 - p0 - p0.5 = 1 - u + up0.5 - p0.5? >I'm a bit interested in the term up0.5 that seems to be superfluous. u is defined by p0 = u * (1 - p0.5). If you replace p0 by u(1 - p0.5) in 1 - p0 - p0.5, the you get 1 - u + up0.5 - p0.5 > >Maybe we should continue via email if no one else shows interest in the >discussions. >I don't know if Uri still follows it, if so shout... > >/Peter We are at the very bottom of the message board now, so I suppose we are not annoying anybody. Rémi
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