Weibull Distribution

Weibull

The Weibull distribution has the probability density function:

\[\begin{split}f(x;k,\theta) = \begin{cases} \frac{k}{\theta} \left( \frac{x}{\theta} \right)^{k-1} \exp\left( -\left(\frac{x}{\theta}\right)^k \right)\,, & x > 0 \,, \\ 0, & \text{otherwise,} \end{cases}\end{split}\]

where \(\theta>0\) is the shape and \(k>0\) the scale parameter. The mean of the Weibull distribution is given by \(\theta\Gamma(1+1/k)\).

Usage

e["Distribution"][*index*]["Type"] = "Univariate/Weibull"

Distribution Configuration

These are settings required by this distribution.

Shape

Usage: e[“Shape”] = real number
Description: The shape of the Weibull distribution.

Scale

Usage: e[“Scale”] = real number
Description: The scale of the Weibull distribution.

Configuration

These are settings required by this module.

Name

Usage: e[“Name”] = string
Description: Defines the name of the distribution.

Random Seed

Usage: e[“Random Seed”] = unsigned integer
Description: Defines the random seed of the distribution.

Range

Usage: e[“Range”] = gsl_rng
Description: Stores the current state of the distribution in hexadecimal notation.

Default Configuration

These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.

{
"Name": "",
"Random Seed": 0,
"Range": ""
}