Modelica.Math.Distributions.TruncatedWeibull

Library of truncated Weibull 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 Weibull distribution. Examples:

For more details
of the Weibull 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 Weibull distribution
cumulative	Cumulative distribution function of truncated Weibull distribution
quantile	Quantile of truncated Weibull distribution

Modelica.Math.Distributions.TruncatedWeibull.density

Density of truncated Weibull distribution

Information

Syntax

Weibull.density(u, u_min=0, u_max=1, lambda=1, k=1);

Description

This function computes the probability density function according to a truncated Weibull distribution with minimum value u_min, maximum value u_max, scale parameter of original distribution lambda and shape parameter of original distribution k. Plot of the function:

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

Example

  density(0.5)             // = 0.9595173756674719
  density(0.5,0,0.8,0.5,2) // = 1.5948036466479143

See also

TruncatedWeibull.cumulative, TruncatedWeibull.quantile.

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

Inputs

Outputs

Modelica.Math.Distributions.TruncatedWeibull.cumulative

Cumulative distribution function of truncated Weibull distribution

Information

Syntax

Weibull.cumulative(u, u_min=0, u_max=1, lambda=1, k=1);

Description

This function computes the cumulative distribution function according to a truncated Weibull distribution with minimum value u_min, maximum value u_max, scale parameter of original distribution lambda and shape parameter of original distribution k. The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

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

Example

  cumulative(0.5)             // = 0.6224593312018546
  cumulative(0.5,0,0.8,0.5,2) // = 0.6850805314988328

See also

TruncatedWeibull.density, TruncatedWeibull.quantile.

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

Inputs

Outputs

Modelica.Math.Distributions.TruncatedWeibull.quantile

Quantile of truncated Weibull distribution

Information

Syntax

Weibull.quantile(u, y_min=0, y_max=1, lambda=1, k=1);

Description

This function computes the inverse cumulative distribution function (= quantile) according to a truncated Weibull distribution with minimum value u_min, maximum value u_max, scale parameter of original distribution lambda and shape parameter of original distribution k. 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 Weibull distribution, see Wikipedia,
of truncated distributions, see Wikipedia.

Example

  quantile(0.001)           // = 0.0006323204312624211;
  quantile(0.5,0,1,0.5,0.9) // = 0.256951787882498

See also

TruncatedWeibull.density, TruncatedWeibull.cumulative.

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

Inputs

Outputs