.Modelica_Noise.Math.Distributions.TruncatedNormal.cumulative

Information

Syntax

Normal.cumulative(u, u_min=0, u_max=1, mu=0, sigma=1);

Description

This function computes the cumulative distribution function according to a truncated normal distribution with minimum value u_min, maximmum value u_max, mean value of original distribution mu and standard deviation of original distribution sigma (variance = sigma²). The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details
of the normal distribution, see Wikipedia,
of truncated distributions, see Wikipedia.

Example

  cumulative(0.5)                 // = 0.5
  cumulative(0.5,-1.5,1.5,1,0.9)  // = 0.4046868865634537

See also

TruncatedNormal.density, TruncatedNormal.quantile.

Interface

function cumulative
  import Modelica_Noise.Math.Distributions.Normal;
  extends Modelica_Noise.Math.Distributions.Interfaces.partialTruncatedCumulative;
  input Real mu = (u_max + u_min)/2 "Expectation (mean) value of the normal distribution" annotation(
    Dialog);
  input Real sigma = (u_max - u_min)/6 "Standard deviation of the normal 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