Ratio of Two Uniform Distribution

UniformRatio

The UniformRatio distribution is the distribution of \(Z=X/Y\), where \(X\) and \(Y\) are two uniformly distributed random variables. The probability density function is:

\[\begin{split}f(z;minX,maxX,minY,maxY)= \begin{cases} (min(maxY, maxX / z)^2 - max(minY, minX / z)^2) * C & z \in [ minX/maxY, maxX/minY ]\,, \\ 0, & \text{otherwise,} \end{cases}\end{split}\]

where \(minX\) and \(maxX\) are the bounds of the random variable X, and \(minY\) and \(maxY\) are the bounds of the random variable Y. \(C\) is a normalization constant.

Usage

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

Distribution Configuration

These are settings required by this distribution.

Minimum X

  • Usage: e[“Minimum X”] = real number

  • Description: Lower bound of the first (dividend) uniform distribution.

Maximum X

  • Usage: e[“Maximum X”] = real number

  • Description: Upper bound of the first (divident) uniform distribution.

Minimum Y

  • Usage: e[“Minimum Y”] = real number

  • Description: Lower bound of the second (divisor) uniform distribution.

Maximum Y

  • Usage: e[“Maximum Y”] = real number

  • Description: Upper bound of the second (divisor) uniform 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": ""
}