distributions
Class CDF_Normal

java.lang.Object
  |
  +--distributions.CDF_Normal

public class CDF_Normal
extends java.lang.Object

This class contains routines to calculate the normal cumulative distribution function (CDF) and its inverse.


Constructor Summary
CDF_Normal()
           
 
Method Summary
static double normp(double z)
          This method calculates the normal cumulative distribution function.
static double xnormi(double p)
          This method calculates the normal cdf inverse function.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

CDF_Normal

public CDF_Normal()
Method Detail

xnormi

public static double xnormi(double p)
This method calculates the normal cdf inverse function.

Let PHI(x) be the normal cdf. Suppose that Q calculates 1.0 - PHI(x), and that QINV calculates QINV(p) for p in (0.0,.5]. Then for p .le. .5, x = PHIINV(p) = -QINV(p). For p .gt. .5, x = PHIINV(p) = QINV(1.0 - p). The formula for approximating QINV is taken from Abramowitz and Stegun, Handbook of Mathematical Functions, Dover, 9th printing, formula 26.2.23, page 933. The error in x is claimed to be less than 4.5e-4 in absolute value.

Parameters:
p - p must lie between 0 and 1. xnormi returns the normal cdf inverse evaluated at p.

normp

public static double normp(double z)
This method calculates the normal cumulative distribution function.

It is based upon algorithm 5666 for the error function, from:

       Hart, J.F. et al, 'Computer Approximations', Wiley 1968

The FORTRAN programmer was Alan Miller. The documentation in the FORTRAN code claims that the function is "accurate to 1.e-15."

Steve Verrill translated the FORTRAN code (the March 30, 1986 version) into Java. This translation was performed on January 10, 2001.

Parameters:
z - The method returns the value of the normal cumulative distribution function at z.