Function ExtremeValue(location, scale)

ExtremeValue

The function ExtremeValue draws a random value from an extreme value distribution.

ExtremeValue(
       location,    ! (optional) numerical expression
       scale        ! (optional) numerical expression
       )

The ExtremeValue(location,scale) distribution provided by AIMMS is a Type I Gumbel (\(\mu\), \(\beta\)) distribution.

Arguments

location

A scalar numerical expression.

scale

A scalar numerical expression \(> 0\).

Return Value

The function ExtremeValue returns a random value drawn from an extreme value distribution with location location and scale scale.

Graph

../../_images/extremevalue.png

A graph with:

  • a histogram for 1.000 experiments of drawing from distribution ExtremeValue(3,4), and

  • the DistributionDensity for ExtremeValue(3,4)

Example

The code:

option seed := 1234 ;
_p_draw := ExtremeValue( 0, 10 )  ;
_p_pointDensity := DistributionDensity( ExtremeValue( 0, 10 ), 3 );

block where listing_number_precision := 6 ;
        display _p_draw, _p_pointDensity ;
endblock ;

will produce

_p_draw := -2.456478 ;
_p_pointDensity := 0.034999 ;

in the listing file.

References