WOLFRAM SYSTEM MODELER

# cumulative

Cumulative distribution function of truncated normal distribution

# Wolfram Language

In[1]:=
`SystemModel["Modelica.Math.Distributions.TruncatedNormal.cumulative"]`
Out[1]:=

# Information

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

#### 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
```

# Syntax

y = cumulative(u, u_min, u_max, mu, sigma)

# Inputs (5)

u Type: Real Description: Value over the real axis (-inf < u < inf) Default Value: 0 Type: Real Description: Lower limit of u Default Value: 1 Type: Real Description: Upper limit of u Default Value: (u_max + u_min) / 2 Type: Real Description: Expectation (mean) value of the normal distribution Default Value: (u_max - u_min) / 6 Type: Real Description: Standard deviation of the normal distribution

# Outputs (1)

y Type: Real Description: Value in the range 0 <= y <= 1

# Revisions

Date Description
June 22, 2015
 Initial version implemented by A. Klöckner, F. v.d. Linden, D. Zimmer, M. Otter. DLR Institute of System Dynamics and Control