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CdfNormal Method
Evaluates the normal (Gaussian) cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
public static double Normal(
	double x
)

Parameters

x
Type: SystemDouble
A double scalar value representing the argument at which the function is to be evaluated.

Return Value

Type: Double
A double scalar value representing the probability that a normal variable takes a value less than or equal to x.
Remarks
Method Cdf.Normal evaluates the distribution function, \Phi, of a standard normal (Gaussian) random variable, that is,
\Phi\left(x\right)=\frac{1}{{\sqrt{2\pi}}
            }\int_{-\infty}^x{}e^{-t^2/2}dt
The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x.

The standard normal distribution (for which Cdf.Normal is the distribution function) has mean of 0 and variance of 1. The probability that a normal random variable with mean \mu
            and variance \sigma^2 is less than y is given by Cdf.Normal evaluated at (y-\mu)/
            \sigma.

\Phi(x) is evaluated by use of the complementary error function, erfc. The relationship is:

\Phi(x)={\rm{erfc}}(-x/\sqrt{2.0})/2

Standard Normal Distribution Function

See Also

Reference

Other Resources