Cdf.ExtremeValue Method

CdfExtremeValue Method

Evaluates the extreme value cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double ExtremeValue(
	double x,
	double mu,
	double beta
)

Public Shared Function ExtremeValue ( 
	x As Double,
	mu As Double,
	beta As Double
) As Double

public:
static double ExtremeValue(
	double x, 
	double mu, 
	double beta
)

static member ExtremeValue : 
        x : float * 
        mu : float * 
        beta : float -> float

Parameters

x: Type: SystemDouble
A double scalar value representing the argument at which the function is to be evaluated.
mu: Type: SystemDouble
A double scalar value representing the location parameter, $\mu$ .
beta: Type: SystemDouble
A double scalar value representing the scale parameter, $\beta$ .

Return Value

Type: Double
A double scalar value representing the probability that an extreme value random variable takes on a value less than or equal to x.

Remarks

Method Cdf.ExtremeValue, also known as the Gumbel minimum distribution, evaluates the extreme value distribution function, F, of a uniform random variable with location parameter $\mu$ and shape parameter $\beta$ ; that is,

$F\left(x\right)=\int_0^x{1-e^{-e^{\frac{ x-\mu}{\beta}}}}dt$

The case where $\mu=0$ and $\beta=1$ is called the standard Gumbel distribution.

Random numbers are generated by evaluating uniform variates , equating the continuous distribution function, and then solving for by first computing $\frac{x_i-\mu}{\beta}=log(-log(1-u_i))$ .

Plot of Extreme Value Distribution Function

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example