NormC(x, m, s) Normal Cumulative Distribution Function

By definition,

NormC(x, m, s) = Integral{-infinity, x} [exp(-((t-m)^2)/(2*s^2))/(s*SqRt(2*Pi)] dt.

It is the probability that a normal random variable with mean m and standard deviation s will be less than x.

It is computed by:

NormC(x, m, s) = (1/2) * ErfC((m - x)/(s*SqRt(2)).

The ErfC function is used to give accurate results when x << m where NormC is very small.

If s is zero, the answer is zero if x < m, one if x > m, and 0.5 if x = m.

If s < 0, the complement is given, NormC(x, m, -s) = 1 - NormC(x, m, s).

If x, m, or s is not real, values are given based on this formula that are not probabilities.

See: Normal Distribution -- From MathWorld

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