.Modelica.Math.Distributions.Normal.quantile

Information

Syntax

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

Description

This function computes the inverse cumulative distribution function (= quantile) according to a normal distribution with mean value mu and standard deviation sigma (variance = sigma²). Input argument u must be in the range:

0 < u < 1

If the input argument u is a uniformly distributed random number, then 99.7 % of the returned random numbers are in the range:

mu-3*sigma ≤ y ≤ mu+3*sigma

Plot of the function:

For more details, see Wikipedia.

Example

  quantile(0.001)     // = -3.090232306167813;
  quantile(0.5,1,0.5) // = 1

See also

Normal.density, Normal.cumulative.

Interface

function quantile
  import Modelica.Math.Special;
  extends Modelica.Math.Distributions.Interfaces.partialQuantile;
  input Real mu = 0 "Expectation (mean) value of the normal distribution" annotation(
    Dialog);
  input Real sigma = 1 "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