Package Modelica.​Math.​Distributions.​Uniform
Library of uniform distribution functions

Information

This package provides

of the uniform distribution. Examples:

For more details of this distribution see Wikipedia.

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

Package Contents

NameDescription
cumulativeCumulative distribution function of uniform distribution
densityDensity of uniform distribution
quantileQuantile of uniform distribution

Function Modelica.​Math.​Distributions.​Uniform.​density
Density of uniform distribution

Information

Syntax

Uniform.density(u, u_min=0, u_max=1);

Description

This function computes the probability density function according to a uniform distribution in a band. Plot of the function:

For more details, see Wikipedia.

Example

  density(0.5)    // = 1
  density(0,-1,1) // = 0.5

See also

Uniform.cumulative, Uniform.quantile.

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

Inputs

TypeNameDescription
RealuRandom number over the real axis (-inf < u < inf)
Realu_minLower limit of u
Realu_maxUpper limit of u

Outputs

TypeNameDescription
RealyDensity of u

Function Modelica.​Math.​Distributions.​Uniform.​cumulative
Cumulative distribution function of uniform distribution

Information

Syntax

Uniform.cumulative(u, u_min=0, u_max=1);

Description

This function computes the cumulative distribution function according to a uniform distribution in a band. The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details, see Wikipedia.

Example

  cumulative(0.5)    // = 0.5
  cumulative(0,-1,1) // = 0.5

See also

Uniform.density, Uniform.quantile.

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

Inputs

TypeNameDescription
RealuValue over the real axis (-inf < u < inf)
Realu_minLower limit of u
Realu_maxUpper limit of u

Outputs

TypeNameDescription
RealyValue in the range 0 <= y <= 1

Function Modelica.​Math.​Distributions.​Uniform.​quantile
Quantile of uniform distribution

Information

Syntax

Uniform.quantile(u, y_min=0, y_max=1);

Description

This function computes the inverse cumulative distribution function (= quantile) according to a uniform distribution in a band. Input argument u must be in the range:

0 ≤ u ≤ 1

The returned number y is in the range:

y_min ≤ y ≤ y_max

Plot of the function:

For more details, see Wikipedia.

Example

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

See also

Uniform.density, Uniform.cumulative.

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

Inputs

TypeNameDescription
RealuRandom number in the range 0 <= u <= 1
Realy_minLower limit of y
Realy_maxUpper limit of y

Outputs

TypeNameDescription
RealyRandom number u transformed according to the given distribution

Generated 2018-12-12 12:14:35 EST by MapleSim.