## 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.