functioncumulative
Cumulative distribution function of truncated normal distribution
Extends from Modelica.Math.Distributions.Interfaces.partialTruncatedCumulative (Common interface of truncated cumulative distribution functions).
Information
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
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | u (from partialCumulative) | Value over the real axis (-inf < u < inf) | |
| Real | u_min (from partialTruncatedCumulative) | 0 | Lower limit of u |
| Real | u_max (from partialTruncatedCumulative) | 1 | Upper limit of u |
| Real | mu | (u_max + u_min)/2 | Expectation (mean) value of the normal distribution |
| Real | sigma | (u_max - u_min)/6 | Standard deviation of the normal distribution |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | y (from partialCumulative) | Value in the range 0 <= y <= 1 |
Revisions
| Date | Description | ||
|---|---|---|---|
| June 22, 2015 |
|
