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NormalInverse Method

Normal (Gaussian) inverse cumulative distribution function.

Namespace:  Accord.Math
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
public static double Inverse(
	double y0
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Type: SystemDouble

Return Value

Type: Double
Returns the value, x, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to x) is equal to the argument y (assumes mean is zero, variance is one).

For small arguments 0 < y < exp(-2), the program computes z = sqrt( -2.0 * log(y) ); then the approximation is x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).

There are two rational functions P/Q, one for 0 < y < exp(-32) and the other for y up to exp(-2). For larger arguments, w = y - 0.5, and x/sqrt(2pi) = w + w^3 * R(w^2)/S(w^2)).

See Also