Error Function

Description

Computes the error function based on the normal distribution.

Usage

erf(x)

Arguments

Details

is defined as

Erf(x) = (2/sqrt(pi)) int_0^x exp(-t^2) dt

so that it is closely related to pnorm.

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.

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="red", 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("red", "blue"),
       lty=c("solid", "dotted"), lwd=1:2) 
## End(Not run)