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Re: Cumulative distribution of Gauss

• To: mathgroup at smc.vnet.net
• Subject: [mg18744] Re: Cumulative distribution of Gauss
• From: Denis Cousineau <decousin at indiana.edu>
• Date: Sat, 17 Jul 1999 02:36:54 -0400
• Organization: Indiana University
• References: <7mjqqb$f2v@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

using mathematica, obtaining values of distributions (gaussian=normal,
or any other) is pretty easy.

the cumulative density function (CDF) of the normal distribution
is define if you importe the continuous distribution package using
	<< Statistics`ContinuousDistributions`

Then, you ask the values you need with
	CDF[NormalDistribution[mu,sigma],x]
where mu and sigma are the mean and standard deviation of the 
gaussian you have in mind (or 0 and 1 for the standard gaussian).

=================================================================
If you are not using Mathematica, then, you may use the function
erf, defined in most not-too-hold programing languages (and in most
c language on unix station). The erf function approximate the
correct integral using fast and very accurate algorithms.

The error function erf(x) is used to approximate the normal=gaussian
standard cumulative function in the following formula:
		1/2 (1 + erf[(x-mu)/(Sqrt(2) sigma)] )

J'espere que ca vous aide. N'hesitez pas si vous avez besoin de plus
d'information.
Denis.

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.
> 
> Thank you for assistance.
> 
> D. SALLIER
> 
> sallier_daniel at wanadoo.fr

-- 

Denis Cousineau, Postdoc           *****************************
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