Cauchy Distribution

Cauchy

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

\[f(x;x_{0},\gamma )={1 \over \pi \gamma }\left({\gamma ^{2} \over (x-x_{0})^{2}+\gamma ^{2}}\right)\]

where \(x_{0}\) is the location parameter, specifying the mode of the distribution, and \(\gamma\) is the scale parameter which specifies the half-width at half-maximum (HWHM).

Usage

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

Distribution Configuration

These are settings required by this distribution.

Location

  • Usage: e[“Location”] = real number

  • Description: Specifies the location of the peak of the distribution.

Scale

  • Usage: e[“Scale”] = real number

  • Description: Specifies the half-width at half-maximum (HWHM)

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": ""
}