inverf(x)
Overview
The inverf function calculates the inverse of the error function \text{erf}^{-1}(x) using the Newton-Raphson method for numerical approximation.
Parameters
| Parameter | Type | Description |
|---|---|---|
x |
Number | The value to find the inverse error function of. Must be in the range [-1, 1]. |
Returns
| Return | Type | Description |
|---|---|---|
inv |
Number | The calculated inverse error function value \text{erf}^{-1}(x) . |
Example
local x = 0.5
local result = StatBook.inverf(x)
print(result) -- Output will be approximately 0.4769
Mathematical Background
The function calculates \text{erf}^{-1}(x) using the Newton-Raphson method for solving equations. The Newton-Raphson formula for iteration is:
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
In this context, f(x) = \text{erf}(x) - a and f'(x) = \frac{2}{\sqrt{\pi}} \exp(-x^2) , where a is the argument passed to module.inverf.