generateBeta(alpha, beta)
Overview
The generateBeta(alpha, beta) function generates a random number that follows a Beta distribution.
Parameters
| Parameter | Type | Description |
|---|---|---|
alpha |
Number | The first shape parameter of the Beta distribution. |
beta |
Number | The second shape parameter of the Beta distribution. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a Beta distribution. |
Example
local result = StatBook.generateBeta(2, 5)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a Beta distribution with shape parameters \alpha and \beta . The Beta distribution is often used in statistics to describe probabilities and proportions.
To generate result , the function first generates two gamma-distributed random variables x and y using the Marsaglia and Tsang method for gamma distribution. The x value is generated with \alpha and \beta set to 1, and y value is generated with \alpha set to beta and \beta set to 1. The function then calculates result using:
result = \frac{x}{x + y}