Package edu.cmu.tetrad.util

Class StatUtils

java.lang.Object

edu.cmu.tetrad.util.StatUtils

public final class StatUtils
extends Object

Contains a number of basic statistical functions. Most methods are overloaded for either long or double arrays. NOTE: Some methods in this class have been adapted from class DStat written by Michael Fanelli, and the routines have been included here by permission. The methods which were adapted are:

• gamma
• internalGamma
• beta
• igamma
• erf
• poisson
• chidist
• contTable1

These methods are protected under copyright by the author. Here is the text of his copyright notice for DSTAT.java: "Copyright 1997 by Michael Fanelli. All Rights Reserved. Unlimited use of this beta code granted for non-commercial use only subject to the the expiration date. Commercial (for profit) use requires written permission."

Version:

$Id: $Id

Author:

josephramsey

Method Summary

Modifier and Type	Method	Description
static double	averageDeviation(double[] array)	averageDeviation.
static double	averageDeviation(double[] array, int N)	averageDeviation.
static double	averageDeviation(long[] array)	averageDeviation.
static double	averageDeviation(long[] array, int N)	averageDeviation.
static double	basisFunctionValue(int type, int index, double x)	Performs a calculation that involves repeatedly multiplying an initial value of `1.0` by the product of `0.95` and a given parameter `x`, iterating `index` times.
static double	beta(double x1, double x2)	Calculates the value of beta for doubles
static double	calculateCentralMoment(double[] data, int i)
static double	calculateCumulant(double[] data, int i)
static double	calculateMoment(double[] data, int i)
static double	chebyshev(int index, double x)	Computes the value of the Chebyshev polynomial of a given degree at a specified point x.
static double	chidist(double x, int degreesOfFreedom)	Calculates the one-tail probability of the Chi-squared distribution for doubles
static short	compressedCorrelation(Vector data1, Vector data2)	compressedCorrelation.
static double	correlation(double[] array1, double[] array2)	correlation.
static double	correlation(double[] array1, double[] array2, int N)	correlation.
static double	correlation(long[] array1, long[] array2)	correlation.
static double	correlation(long[] array1, long[] array2, int N)	correlation.
static double	correlation(Vector data1, Vector data2)	correlation.
static double[]	cov(double[] x, double[] y, double[] condition, double threshold, double direction)	cov.
static double	covariance(double[] array1, double[] array2)	covariance.
static double	covariance(double[] array1, double[] array2, int N)	covariance.
static double	covariance(long[] array1, long[] array2)	covariance.
static double	covariance(long[] array1, long[] array2, int N)	covariance.
static double[][]	covMatrix(double[] x, double[] y, double[][] z, double[] condition, double threshold, double direction)	covMatrix.
static int	dieToss(int n)	dieToss.
static double[]	E(double[] x, double[] y, double[] condition, double threshold, double direction)	E.
static double	entropy(int numBins, double[] _f)	entropy.
static double	erf(double x)	Calculates the error function for a double
static double	expScore(double[] _f)	expScore.
static double	factorial(int c)	factorial.
static int	fdr(double alpha, List<Double> pValues)	fdr.
static int	fdr(double alpha, List<Double> pValues, boolean negativelyCorrelated, boolean pSorted)	fdr.
static double	fdrCutoff(double alpha, List<Double> pValues, boolean negativelyCorrelated)	fdrCutoff.
static double	fdrCutoff(double alpha, List<Double> pValues, boolean negativelyCorrelated, boolean pSorted)	Calculates the cutoff value for p-values using the FDR method.
static double	fdrCutoff(double alpha, List<Double> pValues, int[] _k, boolean negativelyCorrelated, boolean pSorted)	fdrCutoff.
static double	fdrQ(List<Double> pValues, int k)	fdrQ.
static double	gamma(double z)	GAMMA FUNCTION (From DStat, used by permission).
static double[]	getRanks(double[] arr)	getRanks.
static List<Integer>	getRows(double[] x, double[] condition, double threshold, double direction)	getRows.
static List<Integer>	getRows(double[] x, double threshold, double direction)	getRows.
static double	getZForAlpha(double alpha)	getZForAlpha.
static double	hermite1(int index, double x)	Computes the (statitician's) Hermite polynomial of a given index and value.
static double	hermite2(int index, double x)	Computes the (physicis's) Hermite polynomial of a given index and value.
static double	igamma(double a, double x)	Calculates the incomplete gamma function for two doubles
static double	kendallsTau(double[] x, double[] y)	kendallsTau.
static double	kurtosis(double[] array)	kurtosis.
static double	kurtosis(double[] array, int N)	kurtosis.
static double	kurtosis(long[] array)	kurtosis.
static double	kurtosis(long[] array, int N)	kurtosis.
static double	legendre(int index, double x)	Computes the value of the Legendre polynomial of a given degree at a specified point x.
static double	logCoshExp()	logCoshExp.
static double	logCoshScore(double[] _f)	logCoshScore.
static double	logsum(List<Double> logs)	logsum.
static double	max(double[] array)	max.
static double	max(double[] array, int N)	max.
static double	max(long[] array)	max.
static double	max(long[] array, int N)	max.
static double	maxEntApprox(double[] x)	maxEntApprox.
static double	mean(double[] array)	mean.
static double	mean(double[] array, int N)	mean.
static double	mean(long[] array)	mean.
static double	mean(long[] array, int N)	mean.
static double	mean(Vector data, int N)	mean.
static double	meanAbsolute(double[] _f)	meanAbsolute.
static double	median(double[] array)	median.
static double	median(double[] array, int N)	median.
static double	median(long[] array)	median.
static long	median(long[] array, int N)	median.
static double	min(double[] array)	min.
static double	min(double[] array, int N)	min.
static double	min(long[] array)	min.
static double	min(long[] array, int N)	min.
static double	mu(double[] array)	mu.
static double	mu(double[] array, int N)	mu.
static double	mu(long[] array)	mu.
static double	mu(long[] array, int N)	mu.
static double	muHat(double[] array)	muHat.
static double	muHat(double[] array, int N)	muHat.
static double	muHat(long[] array)	muHat.
static double	muHat(long[] array, int N)	muHat.
static int	N(double[] array)	N.
static int	N(long[] array)	N.
static double	partialCorrelation(Matrix submatrix)	Assumes that the given covariance matrix was extracted in such a way that the order of the variables (in either direction) is X, Y, Z1, ..., Zn, where the partial correlation one wants is correlation(X, Y | Z1,...,Zn).
static double	partialCorrelation(Matrix covariance, int x, int y, int... z)	partialCorrelation.
static double	partialCorrelationPrecisionMatrix(Matrix submatrix)	partialCorrelationPrecisionMatrix.
static double	partialCovarianceWhittaker(Matrix submatrix)	Assumes that the given covariance matrix was extracted in such a way that the order of the variables (in either direction) is X, Y, Z1, ..., Zn, where the partial covariance one wants is covariance(X, Y | Z1,...,Zn).
static double	partialCovarianceWhittaker(Matrix covariance, int x, int y, int... z)	partialCovarianceWhittaker.
static double	partialStandardDeviation(Matrix covariance, int x, int... z)	partialStandardDeviation.
static double	partialVariance(Matrix covariance, int x, int... z)	partialVariance.
static double	poisson(double k, double x, boolean cum)	Calculates the Poisson Distribution for mean x and k events for doubles.
static double	pow()	pow.
static double	quartile(double[] array, int quartileNumber)	quartile.
static double	quartile(double[] array, int N, int quartileNumber)	quartile.
static double	quartile(long[] array, int quartileNumber)	quartile.
static double	quartile(long[] array, int N, int quartileNumber)	quartile.
static double	range(double[] array)	range.
static double	range(double[] array, int N)	range.
static double	range(long[] array)	range.
static double	range(long[] array, int N)	range.
static double	rankCorrelation(double[] arr1, double[] arr2)	rankCorrelation.
static double[]	removeNaN(double[] x1)	removeNaN.
static double	sd(double[] array)	sd.
static double	sd(double[] array, int N)	sd.
static double	sd(long[] array)	sd.
static double	sd(long[] array, int N)	sd.
static double	skewness(double[] array)	skewness.
static double	skewness(double[] array, int N)	skewness.
static double	skewness(long[] array)	skewness.
static double	skewness(long[] array, int N)	skewness.
static double	sSquare(double[] array)	sSquare.
static double	sSquare(double[] array, int N)	sSquare.
static double	sSquare(long[] array)	sSquare.
static double	sSquare(long[] array, int N)	sSquare.
static double	ssx(double[] array)	ssx.
static double	ssx(double[] array, int N)	ssx.
static double	ssx(long[] array)	ssx.
static double	ssx(long[] array, int N)	ssx.
static double[]	standardizeData(double[] data)	standardizeData.
static double	standardizedFifthMoment(double[] array)	standardizedFifthMoment.
static double	standardizedFifthMoment(double[] array, int N)	standardizedFifthMoment.
static double	standardizedSixthMoment(double[] array)	standardizedSixthMoment.
static double	standardizedSixthMoment(double[] array, int N)	standardizedSixthMoment.
static double	sum(double[] x)	sum.
static double	sxy(double[] array1, double[] array2)	sxy.
static double	sxy(double[] array1, double[] array2, int N)	sxy.
static double	sxy(long[] array1, long[] array2)	sxy.
static double	sxy(long[] array1, long[] array2, int N)	sxy.
static double	sxy(Vector data1, Vector data2, int N)	sxy.
static double	varHat(double[] array)	varHat.
static double	varHat(double[] array, int N)	varHat.
static double	varHat(long[] array)	varHat.
static double	varHat(long[] array, int N)	varHat.
static double	variance(double[] array)	variance.
static double	variance(double[] array, int N)	variance.
static double	variance(long[] array)	variance.
static double	variance(long[] array, int N)	variance.

Methods inherited from class java.lang.Object

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

Method Details

mean

public static double mean(long[] array)

mean.

Parameters:

array - a long array.

Returns:

the mean of the values in this array.

mean

public static double mean(double[] array)

mean.

Parameters:

array - a double array.

Returns:

the mean of the values in this array.

mean

public static double mean(long[] array,
 int N)

mean.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the mean of the first N values in this array.

mean

public static double mean(double[] array,
 int N)

mean.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the mean of the first N values in this array.

mean

public static double mean(Vector data,
 int N)

mean.

Parameters:

data - a column vector.

N - the number of values of array which should be considered.

Returns:

the mean of the first N values in this array.

median

public static double median(long[] array)

median.

Parameters:

array - a long array.

Returns:

the median of the values in this array.

median

public static double median(double[] array)

median.

Parameters:

array - a double array.

Returns:

the median of the values in this array.

median

public static long median(long[] array,
 int N)

median.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the median of the first N values in this array.

median

public static double median(double[] array,
 int N)

median.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the median of the first N values in this array.

quartile

public static double quartile(long[] array,
 int quartileNumber)

quartile.

Parameters:

array - a long array.

quartileNumber - 1, 2, or 3.

Returns:

the requested quartile of the values in this array.

quartile

public static double quartile(double[] array,
 int quartileNumber)

quartile.

Parameters:

array - a double array.

quartileNumber - 1, 2, or 3.

Returns:

the requested quartile of the values in this array.

quartile

public static double quartile(long[] array,
 int N,
 int quartileNumber)

quartile.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

quartileNumber - 1, 2, or 3.

Returns:

the requested quartile of the first N values in this array.

quartile

public static double quartile(double[] array,
 int N,
 int quartileNumber)

quartile.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

quartileNumber - 1, 2, or 3.

Returns:

the requested quartile of the first N values in this array.

min

public static double min(long[] array)

min.

Parameters:

array - a long array.

Returns:

the minimum of the values in this array.

min

public static double min(double[] array)

min.

Parameters:

array - a double array.

Returns:

the minimum of the values in this array.

min

public static double min(long[] array,
 int N)

min.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the minimum of the first N values in this array.

min

public static double min(double[] array,
 int N)

min.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the minimum of the first N values in this array.

max

public static double max(long[] array)

max.

Parameters:

array - a long array.

Returns:

the maximum of the values in this array.

max

public static double max(double[] array)

max.

Parameters:

array - a double array.

Returns:

the maximum of the values in this array.

max

public static double max(long[] array,
 int N)

max.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the maximum of the first N values in this array.

max

public static double max(double[] array,
 int N)

max.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the maximum of the first N values in this array.

range

public static double range(long[] array)

range.

Parameters:

array - a long array.

Returns:

the range of the values in this array.

range

public static double range(double[] array)

range.

Parameters:

array - a double array.

Returns:

the range of the values in this array.

range

public static double range(long[] array,
 int N)

range.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the range of the first N values in this array.

range

public static double range(double[] array,
 int N)

range.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the range of the first N values in this array.

N

public static int N(long[] array)

N.

Parameters:

array - a long array.

Returns:

the length of this array.

N

public static int N(double[] array)

N.

Parameters:

array - a double array.

Returns:

the length of this array.

ssx

public static double ssx(long[] array)

ssx.

Parameters:

array - a long array.

Returns:

the sum of the squared differences from the mean in array.

ssx

public static double ssx(double[] array)

ssx.

Parameters:

array - a double array.

Returns:

the sum of the squared differences from the mean in array.

ssx

public static double ssx(long[] array,
 int N)

ssx.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the sum of the squared differences from the mean of the first N values in array.

ssx

public static double ssx(double[] array,
 int N)

ssx.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the sum of the squared differences from the mean of the first N values in array.

sxy

public static double sxy(long[] array1,
 long[] array2)

sxy.

Parameters:

array1 - a long array.

array2 - a long array, same length as array1.

Returns:

the sum of the squared differences of the products from the products of the sample means for array1 and array2..

sxy

public static double sxy(double[] array1,
 double[] array2)

sxy.

Parameters:

array1 - a double array.

array2 - a double array, same length as array1.

Returns:

the sum of the squared differences of the products from the products of the sample means for array1 and array2..

sxy

public static double sxy(long[] array1,
 long[] array2,
 int N)

sxy.

Parameters:

array1 - a long array.

array2 - a long array.

N - the number of values of array which should be considered.

Returns:

the sum of the squared differences of the products from the products of the sample means for the first N values in array1 and array2..

sxy

public static double sxy(double[] array1,
 double[] array2,
 int N)

sxy.

Parameters:

array1 - a double array.

array2 - a double array.

N - the number of values of array which should be considered.

Returns:

the sum of the squared differences of the products from the products of the sample means for the first N values in array1 and array2..

sxy

public static double sxy(Vector data1,
 Vector data2,
 int N)

sxy.

Parameters:

data1 - a column vector of doubles.

data2 - a column vector of doubles.

N - the number of values of array which should be considered.

Returns:

the sum of the squared differences of the products from the products of the sample means for the first N values in array1 and array2..

variance

public static double variance(long[] array)

variance.

Parameters:

array - a long array.

Returns:

the variance of the values in array.

variance

public static double variance(double[] array)

variance.

Parameters:

array - a double array.

Returns:

the variance of the values in array.

variance

public static double variance(long[] array,
 int N)

variance.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the variance of the first N values in array.

variance

public static double variance(double[] array,
 int N)

variance.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the variance of the first N values in array.

sd

public static double sd(long[] array)

sd.

Parameters:

array - a long array.

Returns:

the standard deviation of the values in array.

sd

public static double sd(double[] array)

sd.

Parameters:

array - a double array.

Returns:

the standard deviation of the values in array.

sd

public static double sd(long[] array,
 int N)

sd.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the standard deviation of the first N values in array.

sd

public static double sd(double[] array,
 int N)

sd.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the standard deviation of the first N values in array.

covariance

public static double covariance(long[] array1,
 long[] array2)

covariance.

Parameters:

array1 - a long array.

array2 - a second long array (same length as array1).

Returns:

the covariance of the values in array.

covariance

public static double covariance(double[] array1,
 double[] array2)

covariance.

Parameters:

array1 - a double array.

array2 - a second double array (same length as array1).

Returns:

the covariance of the values in array.

covariance

public static double covariance(long[] array1,
 long[] array2,
 int N)

covariance.

Parameters:

array1 - a long array.

array2 - a second long array.

N - the number of values to be considered in array1 and array2.

Returns:

the covariance of the first N values in array1 and array2.

covariance

public static double covariance(double[] array1,
 double[] array2,
 int N)

covariance.

Parameters:

array1 - a double array.

array2 - a second double array (same length as array1).

N - the number of values to be considered in array1 and array2.

Returns:

the covariance of the first N values in array1 and array2.

correlation

public static double correlation(long[] array1,
 long[] array2)

correlation.

Parameters:

array1 - a long array.

array2 - a second long array (same length as array1).

Returns:

the Pearson's correlation of the values in array1 and array2.

correlation

public static double correlation(double[] array1,
 double[] array2)

correlation.

Parameters:

array1 - a double array.

array2 - a second double array (same length as array1).

Returns:

the Pearson's correlation of the values in array1 and array2.

correlation

public static double correlation(Vector data1,
 Vector data2)

correlation.

Parameters:

data1 - a Vector object

data2 - a Vector object

Returns:

a double

compressedCorrelation

public static short compressedCorrelation(Vector data1,
 Vector data2)

compressedCorrelation.

Parameters:

data1 - a Vector object

data2 - a Vector object

Returns:

a short

correlation

public static double correlation(long[] array1,
 long[] array2,
 int N)

correlation.

Parameters:

array1 - a long array.

array2 - a second long array.

N - the number of values to be considered in array1 and array2.

Returns:

the Pearson's correlation of the first N values in array1 and array2.

correlation

public static double correlation(double[] array1,
 double[] array2,
 int N)

correlation.

Parameters:

array1 - a double array.

array2 - a second double array.

N - the number of values to be considered in array1 and array2.

Returns:

the Pearson correlation of the first N values in array1 and array2.

rankCorrelation

public static double rankCorrelation(double[] arr1,
 double[] arr2)

rankCorrelation.

Parameters:

arr1 - an array of objects

arr2 - an array of objects

Returns:

a double

kendallsTau

public static double kendallsTau(double[] x,
 double[] y)

kendallsTau.

Parameters:

x - an array of objects

y - an array of objects

Returns:

a double

getRanks

public static double[] getRanks(double[] arr)

getRanks.

Parameters:

arr - an array of objects

Returns:

an array of objects

sSquare

public static double sSquare(long[] array)

sSquare.

Parameters:

array - a long array.

Returns:

the unbaised estimate of the variance of the distribution of the values in array asuming the mean is unknown.

sSquare

public static double sSquare(double[] array)

sSquare.

Parameters:

array - a double array.

Returns:

the unbaised estimate of the variance of the distribution of the values in array asuming the mean is unknown.

sSquare

public static double sSquare(long[] array,
 int N)

sSquare.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the variance of the distribution of the first N values in array asuming the mean is unknown.

sSquare

public static double sSquare(double[] array,
 int N)

sSquare.

Parameters:

array - a double array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the variance of the distribution of the first N values in array asuming the mean is unknown.

varHat

public static double varHat(long[] array)

varHat.

Parameters:

array - a long array.

Returns:

the unbaised estimate of the variance of the distribution of the values in array asuming the mean is known.

varHat

public static double varHat(double[] array)

varHat.

Parameters:

array - a double array.

Returns:

the unbaised estimate of the variance of the distribution of the values in array asuming the mean is known.

varHat

public static double varHat(long[] array,
 int N)

varHat.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the variance of the distribution of the first N values in array asuming the mean is known.

varHat

public static double varHat(double[] array,
 int N)

varHat.

Parameters:

array - a double array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the variance of the distribution of the first N values in array asuming the mean is known.

mu

public static double mu(long[] array)

mu.

Parameters:

array - a long array.

Returns:

the unbaised estimate of the mean of the distribution of the values in array.

mu

public static double mu(double[] array)

mu.

Parameters:

array - a double array.

Returns:

the unbaised estimate of the mean of the distribution of the values in array.

mu

public static double mu(long[] array,
 int N)

mu.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the mean of the distribution of the first N values in array.

mu

public static double mu(double[] array,
 int N)

mu.

Parameters:

array - a double array.

N - the number of values to be considered in array.

Returns:

the unbaised estimate of the mean of the distribution of the first N values in array.

muHat

public static double muHat(long[] array)

muHat.

Parameters:

array - a long array.

Returns:

the maximum likelihood estimate of the mean of the distribution of the values in array.

muHat

public static double muHat(double[] array)

muHat.

Parameters:

array - a double array.

Returns:

the maximum likelihood estimate of the mean of the distribution of the values in array.

muHat

public static double muHat(long[] array,
 int N)

muHat.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the maximum likelihood estimate of the mean of the distribution of the first N values in array.

muHat

public static double muHat(double[] array,
 int N)

muHat.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the maximum likelihood estimate of the mean of the distribution of the first N values in array.

averageDeviation

public static double averageDeviation(long[] array)

averageDeviation.

Parameters:

array - a long array.

Returns:

the average deviation of the values in array.

averageDeviation

public static double averageDeviation(double[] array)

averageDeviation.

Parameters:

array - a double array.

Returns:

the average deviation of the values in array.

averageDeviation

public static double averageDeviation(long[] array,
 int N)

averageDeviation.

Parameters:

array - a long array.

N - the number of values to be considered in array.

Returns:

the average deviation of the first N values in array.

averageDeviation

public static double averageDeviation(double[] array,
 int N)

averageDeviation.

Parameters:

array - a double array.

N - the number of values to be considered in array.

Returns:

the average deviation of the first N values in array.

calculateMoment

public static double calculateMoment(double[] data,
 int i)

calculateCentralMoment

public static double calculateCentralMoment(double[] data,
 int i)

calculateCumulant

public static double calculateCumulant(double[] data,
 int i)

skewness

public static double skewness(long[] array)

skewness.

Parameters:

array - a long array.

Returns:

the skew of the values in array.

skewness

public static double skewness(double[] array)

skewness.

Parameters:

array - a double array.

Returns:

the skew of the values in array.

skewness

public static double skewness(long[] array,
 int N)

skewness.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the skew of the first N values in array.

skewness

public static double skewness(double[] array,
 int N)

skewness.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the skew of the first N values in array.

removeNaN

public static double[] removeNaN(double[] x1)

removeNaN.

Parameters:

x1 - an array of objects

Returns:

an array of objects

kurtosis

public static double kurtosis(long[] array)

kurtosis.

Parameters:

array - a long array.

Returns:

the kurtosis of the values in array.

kurtosis

public static double kurtosis(double[] array)

kurtosis.

Parameters:

array - a double array.

Returns:

the curtosis of the values in array.

kurtosis

public static double kurtosis(long[] array,
 int N)

kurtosis.

Parameters:

array - a long array.

N - the number of values of array which should be considered.

Returns:

the curtosis of the first N values in array.

standardizedFifthMoment

public static double standardizedFifthMoment(double[] array)

standardizedFifthMoment.

Parameters:

array - an array of objects

Returns:

a double

standardizedFifthMoment

public static double standardizedFifthMoment(double[] array,
 int N)

standardizedFifthMoment.

Parameters:

array - an array of objects

N - a int

Returns:

a double

standardizedSixthMoment

public static double standardizedSixthMoment(double[] array)

standardizedSixthMoment.

Parameters:

array - an array of objects

Returns:

a double

standardizedSixthMoment

public static double standardizedSixthMoment(double[] array,
 int N)

standardizedSixthMoment.

Parameters:

array - an array of objects

N - a int

Returns:

a double

kurtosis

public static double kurtosis(double[] array,
 int N)

kurtosis.

Parameters:

array - a double array.

N - the number of values of array which should be considered.

Returns:

the curtosis of the first N values in array.

gamma

public static double gamma(double z)

GAMMA FUNCTION (From DStat, used by permission).

Calculates the value of gamma(double z) using Handbook of Mathematical Functions AMS 55 by Abromowitz page 256.

Parameters:

z - nonnegative double value.

Returns:

the gamma value of z.

beta

public static double beta(double x1,
 double x2)

Calculates the value of beta for doubles

Parameters:

x1 - the first double

x2 - the second double.

Returns:

beta(x1, x2).

igamma

public static double igamma(double a,
 double x)

Calculates the incomplete gamma function for two doubles

Parameters:

a - first double.

x - second double.

Returns:

incomplete gamma of (a, x).

erf

public static double erf(double x)

Calculates the error function for a double

Parameters:

x - argument.

Returns:

error function of this argument.

poisson

public static double poisson(double k,
 double x,
 boolean cum)

Calculates the Poisson Distribution for mean x and k events for doubles. If third parameter is boolean true, the cumulative Poisson function is returned.

Parameters:

k - # events

x - mean

cum - true if the cumulative Poisson is desired.

Returns:

the value of the Poisson (or cumPoisson) at x.

chidist

public static double chidist(double x,
 int degreesOfFreedom)

Calculates the one-tail probability of the Chi-squared distribution for doubles

Parameters:

x - a double

degreesOfFreedom - a int

Returns:

value of Chi at x with the stated degrees of freedom.

dieToss

public static int dieToss(int n)

dieToss.

Parameters:

n - a int

Returns:

a int

fdrCutoff

public static double fdrCutoff(double alpha,
 List<Double> pValues,
 boolean negativelyCorrelated,
 boolean pSorted)

Calculates the cutoff value for p-values using the FDR method. Hypotheses with p-values less than or equal to this cutoff should be rejected according to the test.

Parameters:

alpha - The desired effective significance level.

pValues - An list containing p-values to be tested in positions 0, 1, ..., n. (The rest of the array is ignored.) Note: This array will not be changed by this class. Its values are copied into a separate array before sorting.

negativelyCorrelated - Whether the p-values in the array pValues are negatively correlated (true if yes, false if no). If they are uncorrelated, or positively correlated, a level of alpha is used; if they are not correlated, a level of alpha / SUM_i=1_n(1 / i) is used.

pSorted - a boolean

Returns:

the FDR alpha, which is the first p-value sorted high to low to fall below a line from (1.0, level) to (0.0, 0.0). Hypotheses less than or equal to this p-value should be rejected.

fdrCutoff

public static double fdrCutoff(double alpha,
 List<Double> pValues,
 boolean negativelyCorrelated)

fdrCutoff.

Parameters:

alpha - a double

pValues - a List object

negativelyCorrelated - a boolean

Returns:

a double

fdrCutoff

public static double fdrCutoff(double alpha,
 List<Double> pValues,
 int[] _k,
 boolean negativelyCorrelated,
 boolean pSorted)

fdrCutoff.

Parameters:

alpha - a double

pValues - a List object

_k - an array of objects

negativelyCorrelated - a boolean

pSorted - a boolean

Returns:

a double

fdr

public static int fdr(double alpha,
 List<Double> pValues)

fdr.

Parameters:

alpha - a double

pValues - a List object

Returns:

the index, >=, in the sorted list of p values of which all p values are rejected. It the index is -1, all p values are rejected.

fdr

public static int fdr(double alpha,
 List<Double> pValues,
 boolean negativelyCorrelated,
 boolean pSorted)

fdr.

Parameters:

alpha - a double

pValues - a List object

negativelyCorrelated - a boolean

pSorted - a boolean

Returns:

a int

fdrQ

public static double fdrQ(List<Double> pValues,
 int k)

fdrQ.

Parameters:

pValues - a List object

k - a int

Returns:

a double

partialCovarianceWhittaker

public static double partialCovarianceWhittaker(Matrix submatrix)

Assumes that the given covariance matrix was extracted in such a way that the order of the variables (in either direction) is X, Y, Z1, ..., Zn, where the partial covariance one wants is covariance(X, Y | Z1,...,Zn). This may be extracted using DataUtils.submatrix().

Parameters:

submatrix - a Matrix object

Returns:

the given partial covariance.

partialCovarianceWhittaker

public static double partialCovarianceWhittaker(Matrix covariance,
 int x,
 int y,
 int... z)

partialCovarianceWhittaker.

Parameters:

covariance - a Matrix object

x - a int

y - a int

z - a int

Returns:

the partial covariance(x, y | z) where these represent the column/row indices of the desired variables in covariance

partialVariance

public static double partialVariance(Matrix covariance,
 int x,
 int... z)

partialVariance.

Parameters:

covariance - a Matrix object

x - a int

z - a int

Returns:

a double

partialStandardDeviation

public static double partialStandardDeviation(Matrix covariance,
 int x,
 int... z)

partialStandardDeviation.

Parameters:

covariance - a Matrix object

x - a int

z - a int

Returns:

a double

partialCorrelation

public static double partialCorrelation(Matrix submatrix)
                                 throws org.apache.commons.math3.linear.SingularMatrixException

Assumes that the given covariance matrix was extracted in such a way that the order of the variables (in either direction) is X, Y, Z1, ..., Zn, where the partial correlation one wants is correlation(X, Y | Z1,...,Zn). This may be extracted using DataUtils.submatrix().

Parameters:

submatrix - a Matrix object

Returns:

the given partial correlation.

Throws:

org.apache.commons.math3.linear.SingularMatrixException - if any.

partialCorrelationPrecisionMatrix

public static double partialCorrelationPrecisionMatrix(Matrix submatrix)
                                                throws org.apache.commons.math3.linear.SingularMatrixException

partialCorrelationPrecisionMatrix.

Parameters:

submatrix - a Matrix object

Returns:

a double

Throws:

org.apache.commons.math3.linear.SingularMatrixException - if any.

partialCorrelation

public static double partialCorrelation(Matrix covariance,
 int x,
 int y,
 int... z)

partialCorrelation.

Parameters:

covariance - a Matrix object

x - a int

y - a int

z - a int

Returns:

the partial correlation(x, y | z) where these represent the column/row indices of the desired variables in covariance

logCoshScore

public static double logCoshScore(double[] _f)

logCoshScore.

Parameters:

_f - an array of objects

Returns:

a double

meanAbsolute

public static double meanAbsolute(double[] _f)

meanAbsolute.

Parameters:

_f - an array of objects

Returns:

a double

pow

public static double pow()

pow.

Returns:

a double

expScore

public static double expScore(double[] _f)

expScore.

Parameters:

_f - an array of objects

Returns:

a double

logCoshExp

public static double logCoshExp()

logCoshExp.

Returns:

a double

entropy

public static double entropy(int numBins,
 double[] _f)

entropy.

Parameters:

numBins - a int

_f - an array of objects

Returns:

a double

maxEntApprox

public static double maxEntApprox(double[] x)

maxEntApprox.

Parameters:

x - an array of objects

Returns:

a double

standardizeData

public static double[] standardizeData(double[] data)

standardizeData.

Parameters:

data - an array of objects

Returns:

an array of objects

factorial

public static double factorial(int c)

factorial.

Parameters:

c - a int

Returns:

a double

getZForAlpha

public static double getZForAlpha(double alpha)

getZForAlpha.

Parameters:

alpha - a double

Returns:

a double

logsum

public static double logsum(List<Double> logs)

logsum.

Parameters:

logs - a List object

Returns:

a double

sum

public static double sum(double[] x)

sum.

Parameters:

x - an array of objects

Returns:

a double

cov

public static double[] cov(double[] x,
 double[] y,
 double[] condition,
 double threshold,
 double direction)

cov.

Parameters:

x - an array of objects

y - an array of objects

condition - an array of objects

threshold - a double

direction - a double

Returns:

an array of objects

covMatrix

public static double[][] covMatrix(double[] x,
 double[] y,
 double[][] z,
 double[] condition,
 double threshold,
 double direction)

covMatrix.

Parameters:

x - an array of objects

y - an array of objects

z - an array of objects

condition - an array of objects

threshold - a double

direction - a double

Returns:

an array of objects

getRows

public static List<Integer> getRows(double[] x,
 double threshold,
 double direction)

getRows.

Parameters:

x - an array of objects

threshold - a double

direction - a double

Returns:

a List object

getRows

public static List<Integer> getRows(double[] x,
 double[] condition,
 double threshold,
 double direction)

getRows.

Parameters:

x - an array of objects

condition - an array of objects

threshold - a double

direction - a double

Returns:

a List object

E

public static double[] E(double[] x,
 double[] y,
 double[] condition,
 double threshold,
 double direction)

E.

Parameters:

x - an array of objects

y - an array of objects

condition - an array of objects

threshold - a double

direction - a double

Returns:

an array of objects

hermite1

public static double hermite1(int index,
 double x)

Computes the (statitician's) Hermite polynomial of a given index and value. The Hermite polynomials are a sequence of orthogonal polynomials defined by the Rodrigues formula. They are orthogonal with respect to the weight function exp(-x^2). The Hermite polynomial of index index is denoted H_n(x).

These are coded up to index 20.

Parameters:

index - The index of the Hermite polynomial to be computed. This must be a non-negative integer less than or equal to 20.

x - The value at which the Hermite polynomial is to be evaluated.

Returns:

The computed value of the Hermite polynomial.

Throws:

IllegalArgumentException - if the index is negative or greater than 20.

hermite2

public static double hermite2(int index,
 double x)

Computes the (physicis's) Hermite polynomial of a given index and value. The Hermite polynomials are a sequence of orthogonal polynomials defined by the Rodrigues formula. They are orthogonal with respect to the weight function exp(-x^2). The Hermite polynomial of index n is denoted H_n(x).

Parameters:

index - The index of the Hermite polynomial to be computed. This must be a non-negative integer.

x - The value at which the Hermite polynomial is to be evaluated.

Returns:

The computed value of the Hermite polynomial.

legendre

public static double legendre(int index,
 double x)

Computes the value of the Legendre polynomial of a given degree at a specified point x.

The Legendre polynomial is a solution to Legendre's differential equation and is used in physics and engineering, particularly in problems involving spherical coordinates.

Parameters:

index - the degree of the Legendre polynomial. Must be a non-negative integer.

x - the point at which the Legendre polynomial is evaluated.

Returns:

the value of the Legendre polynomial of the given degree at the specified point x.

Throws:

IllegalArgumentException - if the index is negative.

chebyshev

public static double chebyshev(int index,
 double x)

Computes the value of the Chebyshev polynomial of a given degree at a specified point x.

Parameters:

index - the degree of the Chebyshev polynomial. Must be a non-negative integer.

x - the point at which the Chebyshev polynomial is evaluated.

Returns:

the value of the Chebyshev polynomial of the given degree at the specified point x.

basisFunctionValue

public static double basisFunctionValue(int type,
 int index,
 double x)

Performs a calculation that involves repeatedly multiplying an initial value of `1.0` by the product of `0.95` and a given parameter `x`, iterating `index` times. The type of function used in the calculation is determined by the `type` parameter. The function types are as follows:

1. `g(x) = x^index [Polynomial basis]
2. `g(x) = hermite1(index, x) [Statician's Hermite polynomial]
3. `g(x) = hermite2(index, x) [Physicist's Hermite polynomial]
4. `g(x) = legendre(index, x) [Legendre polynomial]
5. `g(x) = chebyshev(index, x) [Chebyshev polynomial]

Any other value of `type` will result in an `IllegalArgumentException`.

Parameters:

type - The type of function to be used in the calculation.

index - The number of iterations to perform the multiplication.

x - The value to be multiplied by `0.95` in each iteration.

Returns:

The result of the iterative multiplication.