Statistics

java.lang.Object
- keel.Algorithms.Lazy_Learning.Statistics

```
public class Statistics
extends java.lang.Object
```
Class implementing some distributions, tests, etc. The code is mostly adapted from the CERN Jet Java libraries: Copyright 2001 University of Waikato Copyright 1999 CERN - European Organization for Nuclear Research. Permission to use, copy, modify, distribute and sell this software and its documentation for any purpose is hereby granted without fee, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation. CERN and the University of Waikato make no representations about the suitability of this software for any purpose. It is provided "as is" without expressed or implied warranty.

Version:

$Revision: 1.3 $

Author:

peter.gedeck@pharma.Novartis.com, wolfgang.hoschek@cern.ch, Eibe Frank (eibe@cs.waikato.ac.nz), Richard Kirkby (rkirkby@cs.waikato.ac.nz)

Field Summary

Fields
Modifier and Type	Field and Description
`protected static double`	`big` Big number
`protected static double`	`biginv` Inverse big number
`protected static double`	`LOGPI` Logarithm of PI
`protected static double`	`MACHEP` MACHEP constant
`protected static double`	`MAXGAM` Maximun gamma value
`protected static double`	`MAXLOG` Maximum logarithm value
`protected static double`	`MINLOG` Minimum logarithm value
`protected static double[]`	`P0` approximation for 0 <= \|y - 0.5\| <= 3/8
`protected static double[]`	`P1`
`protected static double[]`	`P2`
`protected static double[]`	`Q0`
`protected static double[]`	`Q1`
`protected static double[]`	`Q2`
`protected static double`	`SQRTH` squared root of H
`protected static double`	`SQTPI` squared root of PI

Constructor Summary

Constructors
Constructor and Description

Statistics()

Constructors
Constructor and Description
`Statistics()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`binomialStandardError(double p, int n)` Computes standard error for observed values of a binomial random variable.
`static double`	`chiSquaredProbability(double x, double v)` Returns chi-squared probability for given value and degrees of freedom.
`static double`	`FProbability(double F, int df1, int df2)` Computes probability of F-ratio.
`static double`	`incompleteBeta(double aa, double bb, double xx)` Returns the Incomplete Beta Function evaluated from zero to `xx`.
`static double`	`lnGamma(double x)` Returns natural logarithm of gamma function.
`static void`	`main(java.lang.String[] ops)` Main method for testing this class.
`static double`	`normalInverse(double y0)` Returns the value, `x`, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to `x`) is equal to the argument `y` (assumes mean is zero, variance is one).
`static double`	`normalProbability(double a)` Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to `x` (assumes mean is zero, variance is one).

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - MACHEP
```
protected static final double MACHEP
```
    MACHEP constant
    
    See Also:
    
    Constant Field Values
  - MAXLOG
```
protected static final double MAXLOG
```
    Maximum logarithm value
    
    See Also:
    
    Constant Field Values
  - MINLOG
```
protected static final double MINLOG
```
    Minimum logarithm value
    
    See Also:
    
    Constant Field Values
  - MAXGAM
```
protected static final double MAXGAM
```
    Maximun gamma value
    
    See Also:
    
    Constant Field Values
  - SQTPI
```
protected static final double SQTPI
```
    squared root of PI
    
    See Also:
    
    Constant Field Values
  - SQRTH
```
protected static final double SQRTH
```
    squared root of H
    
    See Also:
    
    Constant Field Values
  - LOGPI
```
protected static final double LOGPI
```
    Logarithm of PI
    
    See Also:
    
    Constant Field Values
  - big
```
protected static final double big
```
    Big number
    
    See Also:
    
    Constant Field Values
  - biginv
```
protected static final double biginv
```
    Inverse big number
    
    See Also:
    
    Constant Field Values
  - P0
```
protected static final double[] P0
```
    approximation for 0 <= |y - 0.5| <= 3/8
  - Q0
```
protected static final double[] Q0
```
  - P1
```
protected static final double[] P1
```
  - Q1
```
protected static final double[] Q1
```
  - P2
```
protected static final double[] P2
```
  - Q2
```
protected static final double[] Q2
```
- Constructor Detail
  - Statistics
```
public Statistics()
```
- Method Detail
  - binomialStandardError
```
public static double binomialStandardError(double p,
                                           int n)
```
    Computes standard error for observed values of a binomial random variable.
    
    Parameters:
    
    p - the probability of success
    
    n - the size of the sample
    
    Returns:
    
    the standard error
  - chiSquaredProbability
```
public static double chiSquaredProbability(double x,
                                           double v)
```
    Returns chi-squared probability for given value and degrees of freedom. (The probability that the chi-squared variate will be greater than x for the given degrees of freedom.)
    
    Parameters:
    
    x - the value
    
    v - the number of degrees of freedom
    
    Returns:
    
    the chi-squared probability
  - FProbability
```
public static double FProbability(double F,
                                  int df1,
                                  int df2)
```
    Computes probability of F-ratio.
    
    Parameters:
    
    F - the F-ratio
    
    df1 - the first number of degrees of freedom
    
    df2 - the second number of degrees of freedom
    
    Returns:
    
    the probability of the F-ratio.
  - normalProbability
```
public static double normalProbability(double a)
```
    Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x (assumes mean is zero, variance is one).
```
                            x
                             -
                   1        | |          2
  normal(x)  = ---------    |    exp( - t /2 ) dt
               sqrt(2pi)  | |
                           -
                          -inf.

             =  ( 1 + erf(z) ) / 2
             =  erfc(z) / 2
 
```
    where z = x/sqrt(2). Computation is via the functions errorFunction and errorFunctionComplement.
    Parameters:
    
    a - the z-value
    
    Returns:
    
    the probability of the z value according to the normal pdf
  - normalInverse
```
public static double normalInverse(double y0)
```
    Returns the value, x, for which the area under the Normal (Gaussian) probability density function (integrated from minus infinity to x) is equal to the argument y (assumes mean is zero, variance is one).
    For small arguments 0 < y < exp(-2), the program computes z = sqrt( -2.0 * log(y) ); then the approximation is x = z - log(z)/z - (1/z) P(1/z) / Q(1/z). There are two rational functions P/Q, one for 0 < y < exp(-32) and the other for y up to exp(-2). For larger arguments, w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
    
    Parameters:
    
    y0 - the area under the normal pdf
    
    Returns:
    
    the z-value
  - lnGamma
```
public static double lnGamma(double x)
```
    Returns natural logarithm of gamma function.
    
    Parameters:
    
    x - the value
    
    Returns:
    
    natural logarithm of gamma function
  - incompleteBeta
```
public static double incompleteBeta(double aa,
                                    double bb,
                                    double xx)
```
    Returns the Incomplete Beta Function evaluated from zero to xx.
    
    Parameters:
    
    aa - the alpha parameter of the beta distribution.
    
    bb - the beta parameter of the beta distribution.
    
    xx - the integration end point.
    
    Returns:
    
    the Incomplete Beta Function
  - main
```
public static void main(java.lang.String[] ops)
```
    Main method for testing this class.
    
    Parameters:
    
    ops - main args.

Class Statistics

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MACHEP

MAXLOG

MINLOG

MAXGAM

SQTPI

SQRTH

LOGPI

big

biginv

P0

Q0

P1

Q1

P2

Q2

Constructor Detail

Statistics

Method Detail

binomialStandardError

chiSquaredProbability

FProbability

normalProbability

normalInverse

lnGamma

incompleteBeta

main