erf | R Documentation |
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.
pnorm
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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