erf: Error Function, and variants

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/family.maths.R

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

1
2
erf(x, inverse = FALSE)
erfc(x, inverse = FALSE)

Arguments

x

Numeric.

inverse

Logical. Of length 1.

Details

Erf(x) is defined as

Erf(x) = (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

1
2
3
4
5
6
7
## 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)

Example output

Loading required package: stats4
Loading required package: splines

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.