This information is part of the Modelica Standard Library maintained by the Modelica Association.

Syntax

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

Description

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

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

Example

  density(0.5)                // = 1.041828977196953
  density(0.5,-1.5,1.5,1,0.9) // = 0.5365495585520803

See also

TruncatedNormal.cumulative, TruncatedNormal.quantile.

y = density(u, u_min, u_max, mu, sigma)

u	Type: Real Description: Random number over the real axis (-inf < u < inf)
u_min	Default Value: 0 Type: Real Description: Lower limit of u
u_max	Default Value: 1 Type: Real Description: Upper limit of u
mu	Default Value: (u_max + u_min) / 2 Type: Real Description: Expectation (mean) value of the normal distribution
sigma	Default Value: (u_max - u_min) / 6 Type: Real Description: Standard deviation of the normal distribution

y	Type: Real Description: Density of u