Function Exponential(lowerbound, scale)

Exponential

The function Exponential draws a random value from an exponential distribution.

Exponential(
      lowerbound      ! (optional) numerical expression
      scale           ! (optional) numerical expression
     )

Arguments

lowerbound

A scalar numerical expression.

scale

A scalar numerical expression \(> 0\).

Return Value

The function Exponential returns a random value drawn from a exponential distribution with lower bound lowerbound and scale scale.

Note

The prototype of this function has changed with the introduction of AIMMS 3.4. In order to run models that still use the original prototype, the option Distribution_compatibility should be set to Aimms_3_0. The original function Exponential(lambda) returns a random value drawn from a exponential distribution with rate \(lambda = 1/scale\) and lower bound \(0\).

Graph

../../_images/exponential.png

A graph with:

  • a histogram for 100.000 experiments of drawing from distribution Exponential(0,1), and

  • the DistributionDensity for Exponential(0,1)

Example

The code:

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

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

will produce

_p_draw := 4.948559 ;
_p_pointDensity := 7.408182 ;

in the listing file.

References