Evaluates the extreme value cumulative probability distribution
function.
Namespace: Imsl.StatAssembly: 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,
.
- beta
- Type: SystemDouble
A double scalar value representing the scale parameter,
.
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
and shape parameter
; that is,
The case where
and
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 .
See Also