.Modelica.Math.Distributions.TruncatedNormal.quantile

Information

Syntax

Normal.quantile(u, y_min=0, y_max=1, mu=0, sigma=1);

Description

This function computes the inverse cumulative distribution function (= quantile) 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). Input argument u must be in the range:

0 < u < 1

Output argument y is in the range:

y_min ≤ y ≤ y_max

Plot of the function:

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

Example

quantile(0.001)           // = 0.001087357613043849;
quantile(0.5,0,1,0.5,0.9) // = 0.5

See also

TruncatedNormal.density, TruncatedNormal.cumulative.

Interface

function quantile
  import Modelica.Math.Distributions.Normal;
  extends Modelica.Math.Distributions.Interfaces.partialTruncatedQuantile;
  input Real mu = (y_max + y_min) / 2 "Expectation (mean) value of the normal distribution" annotation(
    Dialog);
  input Real sigma = (y_max - y_min) / 6 "Standard deviation of the normal distribution" annotation(
    Dialog);
end quantile;

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