`generateLevy(c, mu)`

The generateLevy(c, mu) function generates a random number that follows a Lévy distribution.

Parameter	Type	Description
`c`	Number	The scale parameter for the Lévy distribution. Must be greater than 0.
`mu`	Number	The location parameter for the Lévy distribution.

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

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

The function generates a random number $result$ that follows a Lévy distribution with scale parameter $c$ and location parameter $\mu$ .

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

$f(x; c, \mu) = \sqrt{\frac{c}{2\pi}} \frac{e^{-\frac{c}{2(x - \mu)}}}{(x - \mu)^{3/2}}$

The function uses the Inverse Error Function to generate a random variable that follows the Lévy distribution:

$result = \frac{c}{(\sqrt{2} \times \text{InverseErrorFunction}(2 \times (1 - \text{math.random}/2) - 1))^2} + \mu$