Cdf.Normal Method

Evaluates the normal (Gaussian) cumulative probability distribution function.

public static double Normal(
double x
);

Parameters

x: A double specifying the argument at which the function is to be evaluated.

Return Value

A double specifying the probability that a normal variable takes a value less than or equal to x.

Remarks

Method 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 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 s given by 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

Cdf.Normal Method

Parameters

Return Value

Remarks

See Also