.Modelica.Math.Distributions.TruncatedNormal.density

Information

Syntax

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

Description

This function computes the probability density function according to a truncated normal distribution with minimum value u_min, maximum value u_max, mean value of original distribution mu and standard deviation of original distribution sigma (variance = sigma²). Plot of the function:

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

Example

  density(0.5)                // = 1.041828977196953
  density(0.5,-1.5,1.5,1,0.9) // = 0.5365495585520803

See also

TruncatedNormal.cumulative, TruncatedNormal.quantile.

Interface

function density
  import Modelica.Math.Distributions.Normal;
  extends Modelica.Math.Distributions.Interfaces.partialTruncatedDensity;
  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 density;

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