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

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.

y = quantile(u, mu, sigma)

u	Type: Real Description: Random number in the range 0 <= u <= 1
mu	Default Value: 0 Type: Real Description: Expectation (mean) value of the normal distribution
sigma	Default Value: 1 Type: Real Description: Standard deviation of the normal distribution

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