13.3.4.6 The Error Function

Submitted by admin on Mon, 2007-11-19 05:29

13.3.4.6  The Error Function

The error function erf(x) gives the integral of the frequently used Gaussian probability distribution. It calculates the estimate that the probability of an observation falls within x standard deviations of the mean, assuming the observations follow a normal distribution. The error function and its variations are central to many calculations in statistics. The error function is also used in solutions of partial differential equations, probability theory, Monte Carlo simulations, and for calculating electrostatic lattice constants. The error function erf(x) is defined as given below.

 

                     

It can be shown that

 

                     

The Math::Cephes error function erf(x) is called erf.