Function Pareto(Shape, Location, Scale)

Pareto

The function Pareto draws a random value from a Pareto distribution.

Pareto(
      Shape,           ! (input) numerical expression
      Location,        ! (optional) numerical expression
      Scale            ! (optional) numerical expression
      )

Arguments

Shape

A scalar numerical expression \(> 0\).

Location

A scalar numerical expression.

Scale

A scalar numerical expression \(> 0\).

Return Value

The function Pareto returns a random value drawn from a Pareto distribution with shape Shape, location Location 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 Pareto(s, beta) returns a random value drawn from a Pareto distribution with shape beta, location \(0\) and scale s.

Graph

../../_images/pareto.png

A graph with:

  • a histogram for 100 experiments of drawing from distribution Pareto(2,0,10), and

  • the DistributionDensity for Pareto(2,0,10)

Example

The code:

option seed := 1234 ;
_p_draw := Pareto( 2, 0, 1 )  ;
_p_pointDensity := DistributionDensity( Pareto( 2, 0, 1 ), 2 );

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

will produce

_p_draw := 1.262422 ;
_p_pointDensity := 0.250000 ;

in the listing file.

References