ERF Function

Returns the value of the (normal) error function.

Categories:	Mathematical
	CAS

Table of Contents

Syntax

ERF(argument)

Required Argument

argument

specifies a numeric constant, variable, or expression.

Details

The ERF function returns the integral, given by

multiline equation line 1 upper E upper R upper F left-parenthesis x right-parenthesis equals StartFraction 2 Over RootIndex StartRoot pi EndRoot EndFraction integral Subscript 0 Superscript x Baseline epsilon Superscript negative z squared Baseline d z

Example

You can use the ERF function to find the probability (p) that a normally distributed random variable with mean 0 and standard deviation will take on a value less than X. For example, the quantity that is given by the following statement is equivalent to PROBNORM(X):

p=.5+.5*erf(x/sqrt(2));

The following SAS statements produce these results:

SAS Statement	Result
y=erf(1.0);	0.8427007929
y=erf(-1.0);	-0.842700793

Last updated: March 16, 2017