R: Error Function, and variants

erf {VGAM} | R Documentation

## Error Function, and variants

### 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

    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).

### Author(s)

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.

### See Also

`pnorm`.

### Examples

    ## 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)

[Package VGAM version 1.0-3 Index]