VGAM (version 1.1-9)

erf: 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)

Value

Returns the value of the function evaluated at x.

Arguments

x

Numeric.

inverse

Logical. Of length 1.

Author

T. W. Yee

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 \((-1,1)\).

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

if (FALSE) {
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) }