quantile

Quantile of truncated 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, 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.

Syntax

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

Inputs (5)

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

Outputs (1)

y

Type: Real

Description: Random number u transformed according to the given distribution