com.aquafold.openapi.math
Interface AQStat

public interface AQStat

Method Summary

double[]	ANOVA(double[][] x) Calculates one way ANOVA for incoming series of arrays [link]
boolean	ANOVATest(double[][] x, double significanceLevel) Performs one way ANOVA Test for incoming series of arrays [link]
double[]	bins(double[] x, int binNumber) Sorts incoming data into user defined number of uniformly spaced bins [link]
double	Chi2(double[] expected, long[] observed) Performs a Pearson's Chi2 test on incoming array.
double[][]	correlation(double[][] x) Calculates correlation matrix of incoming double precision MxN array.
double	correlation(double[] x, double[] y) Calculates the Pearson's correlation coefficient from 2 data sets, and the associated t-test and p-values.
double[][]	covariance(double[][] x) Calculates covariance matrix of incoming double precision MxN array [link]
double	covariance(double[] x, double[] y) Calculates the covariance coefficient from 2 data sets [link]
double	cumNormalDist(double z) Calculates value of cumulative normal distribution at z [link]
double[][]	frequency(double[] x) Calculates values to be displayed in frequency table.
String	frequencyTable(double[] x) Calculates frequency table for incoming array.
double	geometricMean(double[] in) Calculates geometric mean of incoming array.
double	harmonicMean(double[] in) Calculates harmonic mean of incoming array.
double	interquartilerange(double[] in) Calculates difference between 25th and 75th quartile of incoming array.
double	kruskalWallis(double[][] x) Performs Kruskal-Wallis one way ANOVA.
double	kurtosis(double[] in) Calculates kurtosis of incoming array.
double[]	mannWhitneyU(double[] x, double[] y) Performs Mann-Whitney U test.
double	max(double[] in) Calculates maximum value in incoming array.
double	mean(double[] in) Calculates the arithmetic mean of incoming array.
double	median(double[] in) Calculates median value in incoming array.
double	min(double[] in) Calculates minimum value in incoming array.
double	mode(double[] in) Calculates mode of incoming array.
double	pairedTTest(double[] x, double[] y) Performs a paired sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0.
double	percentile(double[] in, double k) Calculates value of kth percentile of incoming array [link]
double	range(double[] in) Calculates range of incoming array.
double	rSquared(double[] x, double[] y) Calculates coefficient of determination (R2).
double	signedRank(double[] x, double M) Performs a signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x comes from a continuous, symmetric distribution with median M, against the alternative that the distribution does not have median M.
double	signedRank(double[] x, double[] y) Performs a paired, signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x-y come from a continuous, symmetric distribution with equal medians, against the alternative that the distribution does not have equal medians.
double	skew(double[] in) Calculates skew (symmetry) of incoming array.
double	spearman(double[] x, double[] y) Calculates the Spearman rank correlation coefficient from 2 data sets [link]
double	sse(double[] in) Calculates the sum squared error of incoming array.
double	std(double[] in) Calculates standard deviation of incoming array.
double	tTest(double[] x) Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0.
double	tTest(double[] x, double m) Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and unknown variance, against the alternative that the mean is not m.
double	tTest(double[] x, double[] y) performs a t-test of the null hypothesis that data in the vectors x and y are independent random samples from normal distributions with equal means and equal but unknown variances, against the alternative that the means are not equal.
double	variance(double[] in) Calculates variance of incoming array.
double[]	zscore(double[] in) Calculates z-scores of incoming array.
double	ztest(double[] x, double mu, double sigma) Performs a z-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and standard deviation sigma, against the alternative that the mean is not m.

Method Detail

mean

double mean(double[] in)

Calculates the arithmetic mean of incoming array. [link]

Parameters:

in - A double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

range

double range(double[] in)

Calculates range of incoming array. Differece between min and max values. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

std

double std(double[] in)

Calculates standard deviation of incoming array. Measures variability of incoming data. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

variance

double variance(double[] in)

Calculates variance of incoming array. Measures variability of incoming data. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

kurtosis

double kurtosis(double[] in)

Calculates kurtosis of incoming array. Degree to which data departs from a normal distribution, in terms of "peakedness." A normal distribution has kurtosis of 1. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

skew

double skew(double[] in)

Calculates skew (symmetry) of incoming array. Degree to which data is centered about the mean. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

median

double median(double[] in)

Calculates median value in incoming array. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

mode

double mode(double[] in)

Calculates mode of incoming array. Most commonly occurring value. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

max

double max(double[] in)

Calculates maximum value in incoming array.

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

min

double min(double[] in)

Calculates minimum value in incoming array.

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

sse

double sse(double[] in)

Calculates the sum squared error of incoming array. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

harmonicMean

double harmonicMean(double[] in)

Calculates harmonic mean of incoming array. The reciprocal of the average of the reciprocals of incoming data points. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

geometricMean

double geometricMean(double[] in)

Calculates geometric mean of incoming array. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

zscore

double[] zscore(double[] in)

Calculates z-scores of incoming array. Indicates number of standard deviations away from mean a value is. [link]

Parameters:

in - a double precision array.

Returns:

double precision array

Throws:

IllegalArgumentException - if the incoming array is empty

interquartilerange

double interquartilerange(double[] in)

Calculates difference between 25th and 75th quartile of incoming array. [link]

Parameters:

in - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

percentile

double percentile(double[] in,
                  double k)

Calculates value of kth percentile of incoming array [link]

Parameters:

in - a double precision array.

k - a double value between 0 and 100

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

frequency

double[][] frequency(double[] x)

Calculates values to be displayed in frequency table. [link]

Parameters:

x - a double precision array.

Returns:

double precision array with 2 columns

• out[0] = List of unique values in incoming array
• out[1] = Number of occurrences of each unique value

Throws:

IllegalArgumentException - if the incoming array is empty

frequencyTable

String frequencyTable(double[] x)

Calculates frequency table for incoming array. [link]

Parameters:

x - a double precision array.

Returns:

String

• List of unique values in incoming array
• Number of occurrences of each unique value
• Relative percentage of each unique value
• Cumulative percentage of each unique value

Throws:

IllegalArgumentException - if the incoming array is empty

rSquared

double rSquared(double[] x,
                double[] y)

Calculates coefficient of determination (R²). Indicates proportion of variance of one variable that can be predicted from a second variable. [link]

• Indicates proportion of variance of one variable that can be predicted from a second variable.
• also used to indicate goodness of fit for regressions and least-squares fittings.

  Parameters:

  x - a double precision array.

  y - a double precision array.

  Returns:

  double precision value

  Throws:

  IllegalArgumentException - if the incoming array is empty

tTest

double tTest(double[] x)

Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0. [link]

Parameters:

x - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

tTest

double tTest(double[] x,
             double m)

Performs a single sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and unknown variance, against the alternative that the mean is not m. I.e. T tests determine whether data sets are likely to have come from populations having the same mean, assuming normal distribution. [link]

Parameters:

x - a double precision array.

m - a double value

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

pairedTTest

double pairedTTest(double[] x,
                   double[] y)

Performs a paired sample t-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean 0 and unknown variance, against the alternative that the mean is not 0. [link]

Parameters:

x - a double precision array.

y - a double precision array

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

tTest

double tTest(double[] x,
             double[] y)

performs a t-test of the null hypothesis that data in the vectors x and y are independent random samples from normal distributions with equal means and equal but unknown variances, against the alternative that the means are not equal. [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

ztest

double ztest(double[] x,
             double mu,
             double sigma)

Performs a z-test of the null hypothesis that data in the vector x are a random sample from a normal distribution with mean m and standard deviation sigma, against the alternative that the mean is not m. [link]

Parameters:

x - a double precision array.

mu - a double precision value

sigma - a double precision value

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

signedRank

double signedRank(double[] x,
                  double M)

Performs a signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x comes from a continuous, symmetric distribution with median M, against the alternative that the distribution does not have median M. [link]

Parameters:

x - a double precision array.

M - a double precision value

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

signedRank

double signedRank(double[] x,
                  double[] y)

Performs a paired, signed rank test (Wilcoxon signed rank) of the null hypothesis that data in the vector x-y come from a continuous, symmetric distribution with equal medians, against the alternative that the distribution does not have equal medians. [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

correlation

double correlation(double[] x,
                   double[] y)

Calculates the Pearson's correlation coefficient from 2 data sets, and the associated t-test and p-values. 1 indicates proportionality. -1 indicates negative proportionality. 0 indicates no correlation. [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

correlation

double[][] correlation(double[][] x)

Calculates correlation matrix of incoming double precision MxN array. [link]

Parameters:

x - an MxN double precision array.

• columns = variables
• rows = observations

Returns:

NxN double precision array

Throws:

IllegalArgumentException - if the incoming array is empty

covariance

double covariance(double[] x,
                  double[] y)

Calculates the covariance coefficient from 2 data sets [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

covariance

double[][] covariance(double[][] x)

Calculates covariance matrix of incoming double precision MxN array [link]

Parameters:

x - an MxN double precision array.

• columns = variables
• rows = observations

Returns:

NxN double precision array

Throws:

IllegalArgumentException - if the incoming array is empty

spearman

double spearman(double[] x,
                double[] y)

Calculates the Spearman rank correlation coefficient from 2 data sets [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

kruskalWallis

double kruskalWallis(double[][] x)

Performs Kruskal-Wallis one way ANOVA. Kruskal Wallis ANOVA is a non-parametric method for testing equality of population medians among groups. It is an extension of the Mann Whitney U test to 3 or more groups. [link]

Parameters:

x - an MxN double precision array, M data arrays of length N.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

ANOVA

double[] ANOVA(double[][] x)

Calculates one way ANOVA for incoming series of arrays [link]

Parameters:

x - a double precision array, M (number of data sets) X N (length of each set)

Returns:

double precision array

• out[0] = ANOVA P-value
• out[1] = ANOVA F-value
  Throws:
  IllegalArgumentException - if the incoming array is empty

ANOVATest

boolean ANOVATest(double[][] x,
                  double significanceLevel)

Performs one way ANOVA Test for incoming series of arrays [link]

Parameters:

x - a double precision array, M (number of data sets) X N (length of each set)

significanceLevel - a double precision value (0Returns:

Boolean

• False if no significant difference among means of incoming arrays (null hypothesis)
  Throws:
  IllegalArgumentException - if the incoming array is empty

Chi2

double Chi2(double[] expected,
            long[] observed)

Performs a Pearson's Chi² test on incoming array. Calcuates p-value. [link]

• The chi-squared statistic compares the "expected" frequency of a sample with the actual, or "observed" frequency.
• measure of "goodness of fit" between predicted and observed data sets
• measure of independence between data sets

Parameters:

expected - a double precision array.

observed - a long array

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty

bins

double[] bins(double[] x,
              int binNumber)

Sorts incoming data into user defined number of uniformly spaced bins [link]

Parameters:

x - a double precision array.

binNumber - an integer

Returns:

double precision array

Throws:

IllegalArgumentException - if the incoming array is empty

mannWhitneyU

double[] mannWhitneyU(double[] x,
                      double[] y)

Performs Mann-Whitney U test. It's non-parametric test for assessing whether two independent samples of observations come from the same distribution. [link]

Parameters:

x - a double precision array.

y - a double precision array.

Returns:

2XN double precision array

• U value
• z value

Throws:

IllegalArgumentException - if the incoming array is empty

cumNormalDist

double cumNormalDist(double z)

Calculates value of cumulative normal distribution at z [link]

Parameters:

z - a double precision array.

Returns:

double precision value

Throws:

IllegalArgumentException - if the incoming array is empty