Beta Distribution

Beta

The Beta distribution has the probability density function (PDF):

\[f(x;k,\theta) = \frac{x^{\alpha-1}(1-x)^{\beta-1} }{B(\alpha, \beta)} \quad \text{ for } x \in [0,1] \text{ and } \alpha, \beta > 0\]

where \(\alpha\) and \(\beta\) are the shape parameters.

Usage

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

Distribution Configuration

These are settings required by this distribution.

Alpha

  • Usage: e[“Alpha”] = real number

  • Description:

Beta

  • Usage: e[“Beta”] = real number

  • Description:

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": ""
}