Function Triangular(Shape, Minimum, Maximum)

Triangular

The function Triangular draws a random value from a triangular distribution.

Triangular(
     Shape,        ! (input) numerical expression
     Minimum,      ! (optional) numerical expression
     Maximum       ! (optional) numerical expression
     )

Arguments

Shape

A scalar numerical expression.

Minimum

A scalar numerical expression.

Maximum

A scalar numerical expression.

Return Value

The function Triangular returns a random value drawn from a triangular distribution with shape Shape, lower bound Minimum and upper bound Maximum. The argument Shape must satisfy the relation 0<Shape<1.

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 Triangular(a, b, c) returns a random value drawn from a triangular distribution with a lower bound a, likeliest value b and upper bound c. The arguments must satisfy the relation a<b<c. The relation between the arguments Shape and b is given by Shape=(b−a)/(c−a).

Graph

../../_images/pareto.png

A graph with:

  • a histogram for 100 experiments of drawing from distribution Triangular(0.300,0,100), and

  • the DistributionDensity for Triangular(0.300,0,100)

Example

The code:

option seed := 1234 ;
_p_draw := Triangular( 0.3, 0, 100 )  ;
_p_pointDensity := DistributionDensity( Triangular( 0.3, 0, 100  ), 20 );

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

will produce

_p_draw := 40.585179 ;
_p_pointDensity := 0.013333 ;

in the listing file.

References