Standard normal distribution function.
The normal (or Gaussian, or bell-shaped) distribution is defined as:
normalDist(x) = 1/√(2π) $(INTEGRATE -$(INFIN), x) exp( - t2/2) dt = 0.5 + 0.5 * erf(x/sqrt(2)) = 0.5 * erfc(- x/sqrt(2))
To maintain accuracy at values of x near 1.0, use normalDistribution(x) = 1.0 - normalDistribution(-x).
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
Standard normal distribution function.
The normal (or Gaussian, or bell-shaped) distribution is defined as:
normalDist(x) = 1/√(2π) $(INTEGRATE -$(INFIN), x) exp( - t2/2) dt = 0.5 + 0.5 * erf(x/sqrt(2)) = 0.5 * erfc(- x/sqrt(2))
To maintain accuracy at values of x near 1.0, use normalDistribution(x) = 1.0 - normalDistribution(-x).
References: http://www.netlib.org/cephes/ldoubdoc.html, G. Marsaglia, "Evaluating the Normal Distribution", Journal of Statistical Software <b>11</b>, (July 2004).