generateT(df)
Overview
The generateT(df) function generates a random number that follows a Student's t-distribution with df degrees of freedom.
Parameters
| Parameter | Type | Description |
|---|---|---|
df |
Number | The degrees of freedom for the t-distribution. |
Returns
| Return | Type | Description |
|---|---|---|
result |
Number | A random number from a Student's t-distribution. |
Example
local result = StatBook.generateT(10)
print(result) -- Output will vary
Mathematical Background
The function generates a random number result that follows a Student's t-distribution with df degrees of freedom.
The probability density function (pdf) for the Student's t-distribution is:
f(t; df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{df \pi} \Gamma(\frac{df}{2})} \left(1 + \frac{t^2}{df} \right)^{-\frac{df + 1}{2}}
In this implementation, the Student's t-distribution is generated using the formula:
\text{result} = \frac{x}{\sqrt{y / df}}
Where x is a random number from a standard normal distribution and y is a random number from a chi-square distribution with df degrees of freedom.