# erf: Error Function, and variants In VGAM: Vector Generalized Linear and Additive Models

## Description

Computes the error function, or its inverse, based on the normal distribution. Also computes the complement of the error function, or its inverse,

## Usage

 ```1 2``` ```erf(x, inverse = FALSE) erfc(x, inverse = FALSE) ```

## Arguments

 `x` Numeric. `inverse` Logical. Of length 1.

## Details

Erf(x) is defined as

Erf(x) = (2/sqrt(pi)) int_0^x exp(-t^2) dt

so that it is closely related to `pnorm`. The inverse function is defined for x in (-1,1).

## Value

Returns the value of the function evaluated at `x`.

## Note

Some authors omit the term 2/sqrt(pi) from the definition of Erf(x). Although defined for complex arguments, this function only works for real arguments.

The complementary error function erfc(x) is defined as 1-erf(x), and is implemented by `erfc`. Its inverse function is defined for x in (0,2).

T. W. Yee

## References

Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications Inc.

`pnorm`.

## Examples

 ```1 2 3 4 5 6 7``` ```## Not run: curve(erf, -3, 3, col = "orange", ylab = "", las = 1) curve(pnorm, -3, 3, add = TRUE, col = "blue", lty = "dotted", lwd = 2) abline(v = 0, h = 0, lty = "dashed") legend("topleft", c("erf(x)", "pnorm(x)"), col = c("orange", "blue"), lty = c("solid", "dotted"), lwd = 1:2) ## End(Not run) ```

### Example output ```Loading required package: stats4