generateWeibull(alpha, beta)

Overview

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

Parameters

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

Returns

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

Example

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

Mathematical Background

The function generates a random number result that follows a Weibull distribution with scale parameter α and shape parameter β.

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

f(x;α,β)=βαxβ1eαxβfor x0,α>0,β>0

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

result=α(ln(1U))1/β

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