Cumulative distribution function for the Normal distribution, and its complement.
The normal (or Gaussian, or bell-shaped) distribution is defined as:
normalDist(x) = 1/√ π $(INTEGRAL -$(INFINITY), x) exp( - t2/2) dt = 0.5 + 0.5 * erf(x/sqrt(2)) = 0.5 * erfc(- x/sqrt(2))
Note that normalDistribution(x) = 1 - normalDistribution(-x).
Accuracy: Within a few bits of machine resolution over the entire range.
References: http://www.netlib.org/cephes/ldoubdoc.html, G. Marsaglia, "Evaluating the Normal Distribution", Journal of Statistical Software <b>11</b>, (July 2004).
See Implementation
Cumulative distribution function for the Normal distribution, and its complement.
The normal (or Gaussian, or bell-shaped) distribution is defined as:
normalDist(x) = 1/√ π $(INTEGRAL -$(INFINITY), x) exp( - t2/2) dt = 0.5 + 0.5 * erf(x/sqrt(2)) = 0.5 * erfc(- x/sqrt(2))
Note that normalDistribution(x) = 1 - normalDistribution(-x).
Accuracy: Within a few bits of machine resolution over the entire range.
References: http://www.netlib.org/cephes/ldoubdoc.html, G. Marsaglia, "Evaluating the Normal Distribution", Journal of Statistical Software <b>11</b>, (July 2004).