regularizedIncompleteBeta(a, b, x)
Overview
The regularizedIncompleteBeta function calculates the regularized incomplete Beta function I_x(a, b) for given parameters a , b , and x .
Parameters
| Parameter | Type | Description |
|---|---|---|
a |
Number | First parameter of the regularized incomplete Beta function. |
b |
Number | Second parameter of the regularized incomplete Beta function. |
x |
Number | Value at which the regularized incomplete Beta function is evaluated. |
Returns
| Return | Type | Description |
|---|---|---|
regincbeta |
Number | The calculated value of the regularized incomplete Beta function. |
Example
local a = 2.5
local b = 1.5
local x = 0.4
local result = StatBook.regularizedIncompleteBeta(a, b, x)
print(result) -- Output will vary depending on input parameters
Mathematical Background
The regularized incomplete Beta function I_x(a, b) is calculated using the formula:
I_x(a, b) = \frac{{\text{incompleteBeta}(a, b, x)}}{\frac{\Gamma(a) \times \Gamma(b)}{\Gamma(a + b)}}
Here, \text{incompleteBeta}(a, b, x) is the incomplete Beta function and \Gamma is the Gamma function.
The function is a wrapper for the incompleteBeta and Gamma functions, which provide the necessary calculations for the incomplete Beta and Gamma terms in the regularized incomplete Beta function formula.