R: Error Functions and Inverses (Matlab Style)

erf {pracma} | R Documentation

## 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.
`z` | real or complex number; must be a scalar.

### 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.

### Value

Real or complex number(s), the value(s) of the function.

### Note

For the complex error function we used Fortran code from the book S. Zhang & J. Jin “Computation of Special Functions” (Wiley, 1996).

### Author(s)

First version by Hans W Borchers; vectorized version of `erfz` by Michael Lachmann.

### See Also

`pnorm`

### Examples

      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

[Package pracma version 2.0.4 Index]