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

Syntax

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

Description

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

0 < u < 1

Output argument y is in the range:

y_min ≤ y ≤ y_max

Plot of the function:

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

Example

  quantile(0.001)           // = 0.001087357613043849;
  quantile(0.5,0,1,0.5,0.9) // = 0.5

See also

TruncatedNormal.density, TruncatedNormal.cumulative.

y = quantile(u, y_min, y_max, mu, sigma)

u	Type: Real Description: Random number in the range 0 <= u <= 1
y_min	Default Value: 0 Type: Real Description: Lower limit of y
y_max	Default Value: 1 Type: Real Description: Upper limit of y
mu	Default Value: (y_max + y_min) / 2 Type: Real Description: Expectation (mean) value of the normal distribution
sigma	Default Value: (y_max - y_min) / 6 Type: Real Description: Standard deviation of the normal distribution

y	Type: Real Description: Random number u transformed according to the given distribution