Package 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 Contents

Function 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

Function 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

Function 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