ERF

Purpose:

Computes the error function.

Syntax:

ERF(val)

val

-

A scalar, series, or table.

Returns:

A scalar, series, or table.

Example:

erf(1)

 

returns 0.84270079.

Example:

erf(1 + i)

 

returns 1.316151 + 0.190453i

Example:

erfinv(erf(.2))

 

returns 0.2 indicating that ERF and ERFINV are inverse functions.

Example:

erf(-2..0.01..2);

xlabel("x");ylabel("erf(x)");label("Error Function");

 

returns 401 samples of erf(x).

Remarks:

The error function is defined as:

 

image\erf01.gif

 

 

ERF is computed from the FADDEEVA function based on an algorithm developed by Steven G. Johnson. The Faddeeva function is defined as:

 

 

 

 

For a series of measurements described by a normal distribution with a standard deviation of σ and mean value of 0:

 

image\erf02.gif

 

p is the probability that the error of a single measurement lies between -a and +a, for positive a.

 

See PROBN for an implementation of the normal probability distribution function.

See Also:

ERFC

ERFCINV

ERFCX

ERFI

ERFINV

FADDEEVA

PDFNORM

PROBN