.Modelica.Math.Distributions.Weibull.cumulative

Information

Syntax

Weibull.cumulative(u, lambda=1, k=1);

Description

This function computes the cumulative distribution function according to a Weibull distribution with scale parameter lambda and shape parameter k. Equation:

y := if u >= 0 then 1 - exp(-(u/lambda)^k) else 0.0;

The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details, see Wikipedia.

Example

cumulative(0.5)       // = 0.3934693402873666
cumulative(0.5,0.5,1) // = 0.6321205588285577

See also

Weibull.density, Weibull.quantile.

Interface

function cumulative
  import Modelica.Math.Special;
  extends Modelica.Math.Distributions.Interfaces.partialCumulative;
  input Real lambda(min = 0) = 1 "Scale parameter of the Weibull distribution" annotation(
    Dialog);
  input Real k(min = 0) "Shape parameter of the Weibull distribution" annotation(
    Dialog);
end cumulative;

Revisions

Date	Description
June 22, 2015	Initial version implemented by A. Klöckner, F. v.d. Linden, D. Zimmer, M. Otter. DLR Institute of System Dynamics and Control