Cdf.Normal Method

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
)

Public Shared Function Normal ( 
	x As Double
) As Double

public:
static double Normal(
	double x
)

static member Normal : 
        x : float -> float

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

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example