quantile

Quantile of normal distribution

Information

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.

Syntax

y = quantile(u, mu, sigma)

Inputs (3)

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

Outputs (1)

y

Type: Real

Description: Random number u transformed according to the given distribution