erf: Error Function, and variants

In VGAM: Vector Generalized Linear and Additive Models

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) = \frac{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)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.