VGAM (version 0.9-2)

erf: Error Function

Description

Computes the error function based on the normal distribution.

Usage

erf(x)

Arguments

x

Numeric.

Value

• Returns the value of the function evaluated at x.

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.

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

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)