Function LogNormal(Shape, Lowerbound, Scale)

LogNormal

The function LogNormal draws a random value from a lognormal distribution.

LogNormal(
    Shape,        ! (input) numerical expression
    Lowerbound,   ! (optional) numerical expression
    Scale         ! (optional) numerical expression
    )

Arguments

Shape

A scalar numerical expression \(> 0\).

Lowerbound

A scalar numerical expression.

Scale

A scalar numerical expression \(> 0\).

Return Value

The function LogNormal returns a random value drawn from a lognormal distribution with shape Shape, 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 LogNormal(m, sd) returns a random value drawn from a lognormal distribution with mean \(m>0\) and standard deviation \(sd>0\). The same result should now be obtained by setting \(Shape = sd/m\), \(Lowerbound=0\) and \(Scale = m\).

Graph

../../_images/lognormal.png

A graph with:

  • a histogram for 1.000.000 experiments of drawing from distribution LogNormal(4,0,100), and

  • the DistributionDensity for LogNormal(4,0,100)

Example

The code:

option seed := 1234 ;
_p_draw := LogNormal( 4, 0, 1 )  ;
_p_pointDensity := DistributionDensity( LogNormal( 4, 0, 1 ), 3 );

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

will produce

_p_draw := 0.042849 ;
_p_pointDensity := 0.025869 ;

in the listing file.

References