Modelica.Math.Distributions.Weibull

Library of 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 Weibull distribution. Examples:

For more details of this distribution see Wikipedia.

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

Package Content

Name	Description
density	Density of Weibull distribution
cumulative	Cumulative distribution function of Weibull distribution
quantile	Quantile of Weibull distribution

Modelica.Math.Distributions.Weibull.density

Density of Weibull distribution

Information

Syntax

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

Description

This function computes the probability density function according to a Weibull distribution with scale parameter lambda and shape parameter k. Equation:

y = if u >= 0 then (k/lambda)*(u/lambda)^(k - 1)*exp(-(u/lambda)^k) else 0.0;

Plot of the function:

For more details, see Wikipedia.

Example

  density(0.5)     // = 0.36787944117144233
  density(1,0.5,2) // = 0.14652511110987343

See also

Weibull.cumulative, Weibull.quantile.

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

Inputs

Outputs

Modelica.Math.Distributions.Weibull.cumulative

Cumulative distribution function of Weibull distribution

Information

Syntax

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

Description

This function computes the cumulative distribution function according to a Weibull distribution with scale parameter lambda and shape parameter k. Equation:

y := if u >= 0 then 1 - exp(-(u/lambda)^k) else 0.0;

The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details, see Wikipedia.

Example

  cumulative(0.5)       // = 0.3934693402873666
  cumulative(0.5,0.5,1) // = 0.6321205588285577

See also

Weibull.density, Weibull.quantile.

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

Inputs

Outputs

Modelica.Math.Distributions.Weibull.quantile

Quantile of Weibull distribution

Information

Syntax

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

Description

This function computes the inverse cumulative distribution function (= quantile) according to a Weibull distribution with scale parameter lambda and shape parameter k. Equation:

y := lambda * (-log( 1-u)) ^(1/k);

Input argument u must be in the range:

0 ≤ u < 1

Plot of the function:

For more details, see Wikipedia.

Example

  quantile(0)         // = 0
  quantile(0.5,1,0.5) // = 0.41627730557884884

See also

Weibull.density, Weibull.cumulative.

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

Inputs

Outputs