generateBetaPrime(alpha, beta)
Overview
The generateBetaPrime(alpha, beta) function generates a random number that follows a beta prime distribution.
Parameters
| Parameter | Type | Description |
|---|---|---|
alpha |
Number | The shape parameter alpha for the beta prime distribution. Must be greater than 0. |
beta |
Number | The shape parameter beta for the beta prime distribution. Must be greater than 0. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a beta prime distribution. |
Example
local result = StatBook.generateBetaPrime(1, 1)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a beta prime distribution with shape parameters \alpha and \beta .
The Beta Prime distribution is defined as:
f(x;\alpha, \beta) = \frac{x^{\alpha-1}(1+x)^{-\alpha-\beta}}{B(\alpha, \beta)}
where B(\alpha, \beta) is the beta function.
To generate result , the function utilizes the Gamma distribution through two shape parameters \alpha and \beta . It generates two Gamma-distributed random variables y_1 and y_2 with \alpha and \beta respectively. Then, result is computed as:
result = \frac{y_1}{y_2}