Package Modelica.​Math.​Distributions.​TruncatedNormal
Library of truncated normal distribution functions

Information

This package provides

• probability density function (= derivative of cumulative distribution function),
• cumulative distribution function, and
• quantile (= inverse cumulative distribution function).

of the truncated normal distribution. Examples:

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

Extends from Modelica.​Icons.​Package (Icon for standard packages).

Package Contents

Function Modelica.​Math.​Distributions.​TruncatedNormal.​density
Density of truncated normal distribution

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.

Extends from Modelica.​Math.​Distributions.​Interfaces.​partialTruncatedDensity (Common interface of truncated probability density functions).

Inputs

Outputs

Function Modelica.​Math.​Distributions.​TruncatedNormal.​cumulative
Cumulative distribution function of truncated normal distribution

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, maximum 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.

Extends from Modelica.​Math.​Distributions.​Interfaces.​partialTruncatedCumulative (Common interface of truncated cumulative distribution functions).

Inputs

Outputs

Function Modelica.​Math.​Distributions.​TruncatedNormal.​quantile
Quantile of truncated normal distribution

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.

Extends from Modelica.​Math.​Distributions.​Interfaces.​partialTruncatedQuantile (Common interface of truncated quantile functions (= inverse cumulative distribution functions)).

Inputs

Outputs