# erfz: Error Functions and Inverses (Matlab Style)

### Description

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

### Usage

 ```1 2 3 4 5 6 7 8``` ```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.

`pnorm`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` 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 ```

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