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

Syntax

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

Description

This function computes the cumulative distribution 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). The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

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

Example

  cumulative(0.5)                 // = 0.5
  cumulative(0.5,-1.5,1.5,1,0.9)  // = 0.4046868865634537

See also

TruncatedNormal.density, TruncatedNormal.quantile.

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

u	Type: Real Description: Value 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: Value in the range 0 <= y <= 1