edu.illinois.cs.cogcomp.lbjava.util

Class StudentT

java.lang.Object

edu.illinois.cs.cogcomp.lbjava.util.StudentT

public class StudentT
extends Object

A collection of statistical methods supporting computations related to the Student's T distribution.

Date:	2002 as part of Fmath
Amended:	12 May 2003 Statistics separated out from Fmath as a new class
Update:	18 June 2005, 5 January 2006, 25 April 2006, 12, 21 November 2006, 4 December 2006 (renaming of cfd and pdf methods - older version also retained), 31 December 2006, March 2007, 14 April 2007

Documentation

See Michael Thomas Flanagan's Java library on-line web page:
http://www.ee.ucl.ac.uk/~mflanaga /java/Stat.html http://www.ee.ucl.ac.uk/~mflanaga/java/

Copyright © April 2004, June 2005, January 2006, December 2006, April 2007

Permission to Copy

Permission to use, copy and modify this software and its documentation for NON-COMMERCIAL purposes is granted, without fee, provided that an acknowledgement to the author, Michael Thomas Flanagan at www.ee.ucl.ac.uk/~mflanaga, appears in all copies.

Dr. Michael Thomas Flanagan makes no representations about the suitability or fitness of the software for any or for a particular purpose. Michael Thomas Flanagan shall not be liable for any damages suffered as a result of using, modifying or distributing this software or its derivatives.

Author:

Dr. Michael Thomas Flanagan

Field Summary

Fields

Modifier and Type	Field and Description
static double	FPMIN A small number close to the smallest representable floating point number.

Constructor Summary

Constructors

Constructor and Description
StudentT()

Method Summary

Modifier and Type	Method and Description
static double[]	confidenceInterval(double[] x, double alpha) Computes the confidence interval of the specified precision over a set of data points.
static double	contFract(double a, double b, double x) Incomplete fraction summation used in the method regularisedBetaFunction(double,double,double).
static double	factorial(double n) factorial of n.
static double	gamma(double x) Gamma function, Lanczos approximation (6 terms)
static double	logFactorial(double n) log to base e of the factorial of n.
static double	logGamma(double x) log to base e of the Gamma function, Lanczos approximation (6 terms).
static double	regularisedBetaFunction(double z, double w, double x) Regularised Incomplete Beta function.
static double	sign(double x) returns -1 if x < 0 else returns 1 (double version)
static double	studentTcdf(double tValue, int df) Returns the Student's t cumulative distribution function probability
static double	tTable(int df, double alpha) Computes the multiplier for the standard error of the mean when finding a (1 - alpha) * 100% confidence interval.

Methods inherited from class java.lang.Object

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

Field Detail

FPMIN

public static final double FPMIN

A small number close to the smallest representable floating point number.

See Also:

Constant Field Values

Constructor Detail

StudentT

public StudentT()

Method Detail

sign

public static double sign(double x)

returns -1 if x < 0 else returns 1 (double version)

factorial

public static double factorial(double n)

factorial of n. Argument is of type double but must be, numerically, an integer factorial returned as double but is, numerically, should be an integer numerical rounding may makes this an approximation after n = 21

logFactorial

public static double logFactorial(double n)

log to base e of the factorial of n. Argument is of type double but must be, numerically, an integer log[e](factorial) returned as double numerical rounding may makes this an approximation

gamma

public static double gamma(double x)

Gamma function, Lanczos approximation (6 terms)

logGamma

public static double logGamma(double x)

log to base e of the Gamma function, Lanczos approximation (6 terms). Retained for backward compatibility.

contFract

public static double contFract(double a,
                               double b,
                               double x)

Incomplete fraction summation used in the method regularisedBetaFunction(double,double,double). modified Lentz's method

regularisedBetaFunction

public static double regularisedBetaFunction(double z,
                                             double w,
                                             double x)

Regularised Incomplete Beta function. Continued Fraction approximation (see Numerical recipies for details of method)

studentTcdf

public static double studentTcdf(double tValue,
                                 int df)

Returns the Student's t cumulative distribution function probability

tTable

public static double tTable(int df,
                            double alpha)

Computes the multiplier for the standard error of the mean when finding a (1 - alpha) * 100% confidence interval.

Parameters:

df - The degrees of freedom.

alpha - The fraction of the distribution to leave outside the interval.

Returns:

m such that mu +- m s represents a (1 - alpha) * 100% confidence interval, where mu is the sample mean and s is the sample's standard deviation.

confidenceInterval

public static double[] confidenceInterval(double[] x,
                                          double alpha)

Computes the confidence interval of the specified precision over a set of data points.

Parameters:

x - The data points.

alpha - The fraction of the distribution to leave outside the interval.

Returns:

An array containing the mean of the elements in x and half of the size of the confidence interval over x. If this array is named r , then the confidence interval can be stated as r[0] +/- r[1].