`generateWeibull(alpha, beta)`

The generateWeibull(alpha, beta) function generates a random number that follows a Weibull distribution.

Parameter	Type	Description
`alpha`	Number	The scale parameter of the Weibull distribution.
`beta`	Number	The shape parameter of the Weibull distribution.

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

local result = StatBook.generateWeibull(1, 2)
print(result)  -- Output will vary

The function generates a random number $result$ that follows a Weibull distribution with scale parameter $\alpha$ and shape parameter $\beta$ .

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

$f(x; \alpha, \beta) = \beta \alpha x^{\beta - 1} e^{-\alpha x^\beta} \quad \text{for } x \geq 0, \alpha > 0, \beta > 0$

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

$\text{result} = \alpha (-\ln(1 - U))^{1/\beta}$

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