Normal distribution, error function

Normal distribution (also known as Gaussian distribution) is one of the most known continuous distributions. Strictly speaking, there is a set of normal distributions which differs in scale and shift. Hereinafter, by "normal distribution" we imply so called standard normal distribution - normal distribution having mean equal to 0 and standard deviation equal to 1.

Probability density of such normal distribution is:

Cumulative distribution function is expressed using the special function erf(x):

Algorithms

Erf and ErfC subroutines are used to calculate the values of the special function erf(x) and its own complement. Inverse erf function is calculated by using the InvErf subroutine.

Normal distribution's cumulative distribution function is calculated using the NormalDistribution subroutine. Inverse cumulative distribution function is calculated by using the InvNormalDistribution subroutine.

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