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 Content

Name	Description
density	Density of truncated normal distribution
cumulative	Cumulative distribution function of truncated normal distribution
quantile	Quantile of truncated normal distribution

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

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

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