incompleteBeta(a, b, x)
Overview
The incompleteBeta function calculates the incomplete Beta function I_x(a, b) for given parameters a , b , and x .
Parameters
| Parameter | Type | Description |
|---|---|---|
a |
Number | First parameter of the incomplete Beta function. |
b |
Number | Second parameter of the incomplete Beta function. |
x |
Number | Value at which the incomplete Beta function is evaluated. |
Returns
| Return | Type | Description |
|---|---|---|
incbeta |
Number | The calculated value of the incomplete Beta function. |
Example
local a = 2.5
local b = 1.5
local x = 0.4
local result = StatBook.incompleteBeta(a, b, x)
print(result) -- Output will vary depending on input parameters
Mathematical Background
The incomplete Beta function I_x(a, b) is calculated using the formula:
I_x(a, b) = \frac{x^a}{a} \times {}_2F_1(a, 1 - b; a + 1; x)
Here, {}_2F_1(a, 1 - b; a + 1; x) is the hypergeometric function computed by the function hypergeometric2f1(a, b, c, z).
The function is a wrapper for the hypergeometric2f1 function, which provides the necessary calculation for the hypergeometric term in the incomplete Beta function formula.