Error Functions and Inverses (Matlab Style)
The error or Phi function is a variant of the cumulative normal (or Gaussian) distribution.
erf(x) erfinv(y) erfc(x) erfcinv(y) erfcx(x) erfz(z) erfi(z)
x, y |
vector of real numbers. |
z |
real or complex number; must be a scalar. |
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.
Real or complex number(s), the value(s) of the function.
For the complex error function we used Fortran code from the book S. Zhang & J. Jin “Computation of Special Functions” (Wiley, 1996).
First version by Hans W Borchers;
vectorized version of erfz by Michael Lachmann.
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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