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Class weka.core.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
Author:
wolfgang.hoschek@cern.ch
Author:
Eibe Frank (eibe@cs.waikato.ac.nz)
Author:
Richard Kirkby (rkirkby@cs.waikato.ac.nz)

Constructor Index

o Statistics()
 

Method Index

o binomialStandardError(double, int)
Computes standard error for observed values of a binomial random variable.
o chiSquaredProbability(double, double)
Returns chi-squared probability for given value and degrees of freedom.
o FProbability(double, int, int)
Computes probability of F-ratio.
o incompleteBeta(double, double, double)
Returns the Incomplete Beta Function evaluated from zero to xx.
o lnGamma(double)
Returns natural logarithm of gamma function.
o main(String[])
Main method for testing this class.
o normalInverse(double)
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).
o normalProbability(double)
Returns the area under the Normal (Gaussian) probability density function, integrated from minus infinity to x (assumes mean is zero, variance is one).

Constructor Detail

o Statistics
public Statistics()

Method Detail

o 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
o 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
df - the number of degrees of freedom
Returns:
the chi-squared probability
o 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.
o 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
o 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
o lnGamma
public static double lnGamma(double x)
          Returns natural logarithm of gamma function.
Parameters:
x - the value
Returns:
natural logarithm of gamma function
o 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.
o main
public static void main(java.lang.String ops[])
          Main method for testing this class.
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