`generateCauchy(x0, gamma)`

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

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

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

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

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.