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Cumulative distribution function for the normal distribution

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no FrontCover Texts, and no BackCover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

gnuplot source under GPL:
_ln_dnorm(x, m, s) = 0.5 * log(2*pi)  log(s)  0.5*((xm)*1.0/s)**2
dnorm(x, mean, sd) = exp(_ln_dnorm(x, mean, sd))
pnorm(x, mean, sd) = norm((xmean) * 1.0/sd)
set samples 1001
set terminal postscript enhanced colour solid lw 2 "TimesRoman" 20
set output
set xrange [5:5]
set xtics 1
set yrange [0:1]
set ytics 0.1
#f(x,y,z) = dnorm(x, y, sqrt(z)) #use variance, not sd!
#set key 3.8,0.94
f(x,y,z) = pnorm(x, y, sqrt(z))
set key 3.8,0.2
plot \
f(x, 0, 0.2) title "{/Symbol m} = 0, {/Symbol s}^2 = 0.2", \
f(x, 0, 1) title "{/Symbol m} = 0, {/Symbol s}^2 = 1.0", \
f(x, 0, 5) title "{/Symbol m} = 0, {/Symbol s}^2 = 5.0", \
f(x, 2, 0.5) title "{/Symbol m} = 2, {/Symbol s}^2 = 0.5"

This work is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version. This work is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See version 2 and version 3 of the GNU General Public License for more details.http://www.gnu.org/licenses/gpl.htmlGPLGNU General Public Licensetruetrue 
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