generateChiSquare(df)
Overview
The generateChiSquare(df) function generates a random number that follows a Chi-Square distribution with degrees of freedom df.
Parameters
| Parameter | Type | Description |
|---|---|---|
df |
Number | Degrees of freedom for the Chi-Square distribution. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a Chi-Square distribution. |
Example
local result = StatBook.generateChiSquare(5)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a Chi-Square distribution with df degrees of freedom.
The probability density function (pdf) for the Chi-Square distribution is:
f(x; df) = \frac{x^{(df/2 - 1)} e^{-x/2}}{2^{df/2} \Gamma(df/2)} \quad \text{for } x \geq 0, df > 0
In this implementation, the Chi-Square distribution is generated using the gamma distribution:
\text{result} = \text{GenerateGamma}(df / 2, 0.5)