Re: Cumulative distribution of Gauss

*To*: mathgroup at smc.vnet.net*Subject*: [mg18762] Re: [mg18639] Cumulative distribution of Gauss*From*: "Will Cooper" <wcooper1 at san.rr.com>*Date*: Tue, 20 Jul 1999 01:33:25 -0400*Organization*: SouthWest Cable of San Diego, CA*References*: <7mp30t$l8p@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Yes, there is! See the paper by M.K. Simon referenced below where he shows how the CDF of a Gaussian, i.e. Gaussian Q function , Q(x) =1/(2*pi)* Integral(exp(-x^2/2)) dx, x, infinity can be represented by: Q(x) = 1/pi * Integral(exp(-x^2/(2*(sin(Theta))^2)) dTheta, x, pi/2 Ref: Proceedings of the IEEE, Vol 86, No9, Sep 1998 " A Unified Approach to the Performance Analysis of Digital Communications of Generalized Fading Channels", (Eqns.1 & 2, pp1863-1864). Hope this helps, Will Cooper. Tomas Garza wrote in message <7mp30t$l8p at smc.vnet.net>... > D. Sallier (sallier_daniel at wanadoo.fr) wrote: > >> Is there any analytical expression of the cumulative distribution >> of Gauss ? >> If not, can someone provided me with a fast executing algorithm. I am >> currently using pre-tabulated data. It is fine but its ends up to >> be rather >> time consuming for highly iterative calculations. > >Why not try the add-on Statistics package? It looks as if the algorithm for >Gauss cumulative distribution is fast enough. For example, I obtain 10,000 >values in less than 5 seconds: > >In[1]:= >Needs["Statistics`ContinuousDistributions`"] >In[2]:= >dist = NormalDistribution[0, 1] >Out[2]= >NormalDistribution[0, 1] >In[3]:= >Table[CDF[dist, Random[Real, {-3, 3}]], {10000}]; // Timing >Out[3]= >{4.89 Second, Null} > >