Evaluates the extreme value cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double ExtremeValue(
	double x,
	double mu,
	double beta
)
Visual Basic (Declaration)
Public Shared Function ExtremeValue ( _
	x As Double, _
	mu As Double, _
	beta As Double _
) As Double
Visual C++
public:
static double ExtremeValue(
	double x, 
	double mu, 
	double beta
)

Parameters

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

Return Value

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 u_i, equating the continuous distribution function, and then solving for x_i by first computing \frac{x_i-\mu}{\beta}=log(-log(1-u_i)) .

Plot of Extreme Value Distribution Function

See Also