weka.core
Class Statistics

java.lang.Object
  |
  +--weka.core.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: 1.7 $

Author:

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

Constructor Summary

Statistics()

Method Summary

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

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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

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.

main

public static void main(java.lang.String[] ops)

Main method for testing this class.