Package Modelica.​Math.​Distributions.​Normal
Library of 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 normal 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.​Normal.​density
Density of normal distribution

Information

Syntax

Normal.density(u, mu=0, sigma=1);

Description

This function computes the probability density function according to a normal distribution with mean value mu and standard deviation sigma (variance = sigma²). Plot of the function:

For more details, see Wikipedia.

Example

  density(0.5)     // = 0.3520653267642995
  density(3,1,0.5) // = 0.00026766045152977074

See also

Normal.cumulative, Normal.quantile.

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

Inputs

Outputs

Function Modelica.​Math.​Distributions.​Normal.​cumulative
Cumulative distribution function of normal distribution

Information

Syntax

Normal.cumulative(u, mu=0, sigma=1);

Description

This function computes the cumulative distribution function according to a normal distribution with mean value mu and standard deviation sigma (variance = sigma²). The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details, see Wikipedia.

Example

  cumulative(0.5)      // = 0.6914624612740131
  cumulative(0,1,0.5)  // = 0.15865525393145707

See also

Normal.density, Normal.quantile.

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

Inputs

Outputs

Function Modelica.​Math.​Distributions.​Normal.​quantile
Quantile of normal distribution

Information

Syntax

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

Description

This function computes the inverse cumulative distribution function (= quantile) according to a normal distribution with mean value mu and standard deviation sigma (variance = sigma²). Input argument u must be in the range:

0 < u < 1

If the input argument u is a uniformly distributed random number, then 99.7 % of the returned random numbers are in the range:

mu-3*sigma ≤ y ≤ mu+3*sigma

Plot of the function:

For more details, see Wikipedia.

Example

  quantile(0.001)     // = -3.090232306167813;
  quantile(0.5,1,0.5) // = 1

See also

Normal.density, Normal.cumulative.

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

Inputs

Outputs