Error Function, and variants
Computes the error function, or its inverse, based on the normal distribution. Also computes the complement of the error function, or its inverse,
erf(x, inverse = FALSE) erfc(x, inverse = FALSE)
x |
Numeric. |
inverse |
Logical. Of length 1. |
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).
Returns the value of the function evaluated at x.
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).
T. W. Yee
Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications Inc.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.