WOLFRAM SYSTEM MODELER

cumulative

Cumulative distribution function of truncated Weibull distribution

Wolfram Language

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

Information

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

Syntax

Weibull.cumulative(u, u_min=0, u_max=1, lambda=1, k=1);

Description

This function computes the cumulative distribution function according to a truncated Weibull distribution with minimum value u_min, maximum value u_max, scale parameter of original distribution lambda and shape parameter of original distribution k. The returned value y is in the range:

0 ≤ y ≤ 1

Plot of the function:

For more details
of the Weibull distribution, see Wikipedia,
of truncated distributions, see Wikipedia.

Example

cumulative(0.5)             // = 0.6224593312018546
cumulative(0.5,0,0.8,0.5,2) // = 0.6850805314988328

See also

TruncatedWeibull.density, TruncatedWeibull.quantile.

Syntax

y = cumulative(u, u_min, u_max, lambda, k)

Inputs (5)

u

Type: Real

Description: Value over the real axis (-inf < u < inf)

u_min

Default Value: 0

Type: Real

Description: Lower limit of u

u_max

Default Value: 1

Type: Real

Description: Upper limit of u

lambda

Default Value: 1

Type: Real

Description: Scale parameter of the Weibull distribution

k

Type: Real

Description: Shape parameter of the Weibull distribution

Outputs (1)

y

Type: Real

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

Revisions

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