erf
The "error function" or cumulative distribution function is encountered
in probability and can be used to compute the probability that a
Gaussian random number falls within a given range. This algorithm was
taken from the article in the link given immediately below.
http://www4.ncsu.edu/unity/users/p/pfackler/www/ECG790C/accuratecumnorm.pdf
If the above link does not work, an alternate version of the same paper can be found below.
http://www.codeplanet.eu/files/download/accuratecumnorm.pdf
- erf(x)
- Returns the value of erf(x), the "error function" or cumulative distribution function, which computes the probability that a Gaussian random number falls within a given range.
COPY/// erf(x)
//
// Returns the value of erf(x), the "error function" or cumulative
// distribution function, which computes the probability that a
// Gaussian random number falls within a given range.
//
// x value, real
//
/// gmlscripts.pro/license
{
var xAbs, c, e, b;
xAbs = abs(argument0) * sqrt(2);
if (xAbs > 37)
c = 0;
else {
e = exp(-xAbs*xAbs / 2);
if (xAbs < 7.07106781186547) {
b = 0.0352624965998911 * xAbs + 0.700383064443688;
b = b * xAbs + 6.37396220353165;
b = b * xAbs + 33.912866078383;
b = b * xAbs + 112.079291497871;
b = b * xAbs + 221.213596169931;
b = b * xAbs + 220.206867912376;
c = e*b;
b = 0.0883883476483184 * xAbs + 1.75566716318264;
b = b * xAbs + 16.064177579207;
b = b * xAbs + 86.7807322029461;
b = b * xAbs + 296.564248779674;
b = b * xAbs + 637.333633378831;
b = b * xAbs + 793.826512519948;
b = b * xAbs + 440.413735824752;
c /= b;
}
else {
b = xAbs + 0.65;
b = xAbs + 4 / b;
b = xAbs + 3 / b;
b = xAbs + 2 / b;
b = xAbs + 1 / b;
c = e / b / 2.506628274631;
}
}
if (argument0 > 0)
return 1 - 2*c;
else
return 2*c - 1;
}
Contributors: Yourself, brac37
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