VGAM (version 0.7-5)

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

x = seq(-3, 3, len=200)
plot(x, erf(x), type="l", col="red", las=1, lwd=2,
     main="red is erf(x), blue is pnorm(x)")
abline(v=0, h=0, lty="dashed", col="black")
lines(x, pnorm(x), col="blue", lty="dotted", lwd=2)