generateCauchy(x0, gamma)

Overview

The generateCauchy(x0, gamma) function generates a random number that follows a Cauchy distribution.

Parameters

Parameter Type Description
x0 Number The location parameter of the Cauchy distribution.
gamma Number The scale parameter of the Cauchy distribution.

Returns

Return Type Description
result Number A random number from a Cauchy distribution.

Example

local result = StatBook.generateCauchy(0, 1)
print(result)  -- Output will vary

Mathematical Background

The function generates a random number result that follows a Cauchy distribution with location parameter x0 and scale parameter \gamma .

The probability density function (pdf) of the Cauchy distribution is defined as:

f(x; x0, \gamma) = \frac{1}{\pi \gamma [1 + (\frac{x - x0}{\gamma})^2]}

In this implementation, the random variable from the Cauchy distribution is generated using the formula:

\text{result} = x0 + \gamma \tan(\pi (U - 0.5))

where U is a uniformly distributed random number between 0 and 1.