erf: Error Functions and Inverses (Matlab Style)

Description

The error or Phi function is a variant of the cumulative normal (or Gaussian) distribution.

Usage

erf(x)
erfinv(y)
erfc(x)
erfcinv(y)
erfcx(x)
erfz(z)
erfi(z)

Arguments

x, y

vector of real numbers.

real or complex number; must be a scalar.

Value

Real or complex number, the value of the function. Please note that erfz, erfi are not (yet) vectorized.

Details

erf and erfinv are the error and inverse error functions. erfc and erfcinv are the complementary error function and its inverse. erfcx is the scaled complementary error function. erfz is the complex, erfi the imaginary error function.

Examples

Run this code

x <- 1.0
  erf(x); 2*pnorm(sqrt(2)*x) - 1
# [1] 0.842700792949715
# [1] 0.842700792949715
  erfc(x); 1 - erf(x); 2*pnorm(-sqrt(2)*x)
# [1] 0.157299207050285
# [1] 0.157299207050285
# [1] 0.157299207050285
  erfz(x)
# [1] 0.842700792949715
  erfi(x)
# [1] 1.650425758797543