java.lang.Object
org.cicirello.math.stats.Statistics
Utility class of basic statistics.

Method Summary
Modifier and TypeMethodDescriptionstatic double
correlation
(double[] X, double[] Y) Computes correlation coefficient for a pair of random variables.static double
correlation
(int[] X, int[] Y) Computes correlation coefficient for a pair of random variables.static double[][]
correlationMatrix
(double[][] data) Computes correlation matrix.static double[][]
correlationMatrix
(int[][] data) Computes correlation matrix.static double
covariance
(double[] X, double[] Y) Computes covariance for a pair of random variables.static double
covariance
(int[] X, int[] Y) Computes covariance for a pair of random variables.static double
mean
(double[] data) Computes mean of a dataset.static double
mean
(int[] data) Computes mean of a dataset.static double
p
(double t, int dof) Calculates a pvalue from the t statistic and degrees of freedom from a ttest.static double
stdev
(double[] data) Computes the sample standard deviation.static double
stdev
(int[] data) Computes the sample standard deviation.static double
tTestUnequalVariances
(double[] data1, double[] data2) Welch's ttest, also known as ttest with unequal variances.static double
tTestUnequalVariances
(int[] data1, int[] data2) Welch's ttest, also known as ttest with unequal variances.static Number[]
tTestWelch
(double[] data1, double[] data2) Welch's ttest, also known as ttest with unequal variances.static Number[]
tTestWelch
(int[] data1, int[] data2) Welch's ttest, also known as ttest with unequal variances.static double
variance
(double[] data) Computes variance of a population.static double
variance
(int[] data) Computes variance of a population.static double
varianceSample
(double[] data) Computes variance of a sample.static double
varianceSample
(int[] data) Computes variance of a sample.

Method Details

mean
public static double mean(int[] data) Computes mean of a dataset. Parameters:
data
 The dataset. Returns:
 the mean of the data.

mean
public static double mean(double[] data) Computes mean of a dataset. Parameters:
data
 The dataset. Returns:
 the mean of the data.

variance
public static double variance(int[] data) Computes variance of a population. Parameters:
data
 The dataset. Returns:
 the variance of the data.

variance
public static double variance(double[] data) Computes variance of a population. Parameters:
data
 The dataset. Returns:
 the variance of the data.

varianceSample
public static double varianceSample(int[] data) Computes variance of a sample. Parameters:
data
 The dataset. Returns:
 the variance of the data.

varianceSample
public static double varianceSample(double[] data) Computes variance of a sample. Parameters:
data
 The dataset. Returns:
 the variance of the data.

stdev
public static double stdev(int[] data) Computes the sample standard deviation. Parameters:
data
 The dataset. Returns:
 the sample standard deviation.

stdev
public static double stdev(double[] data) Computes the sample standard deviation. Parameters:
data
 The dataset. Returns:
 the sample standard deviation.

covariance
public static double covariance(int[] X, int[] Y) Computes covariance for a pair of random variables. Parameters:
X
 Array of samples of first variable.Y
 Array of samples of second variable. Returns:
 the covariance of X and Y.

covariance
public static double covariance(double[] X, double[] Y) Computes covariance for a pair of random variables. Parameters:
X
 Array of samples of first variable.Y
 Array of samples of second variable. Returns:
 the covariance of X and Y.

correlation
public static double correlation(int[] X, int[] Y) Computes correlation coefficient for a pair of random variables. Parameters:
X
 Array of samples of first variable.Y
 Array of samples of second variable. Returns:
 the correlation coefficient of X and Y.

correlation
public static double correlation(double[] X, double[] Y) Computes correlation coefficient for a pair of random variables. Parameters:
X
 Array of samples of first variable.Y
 Array of samples of second variable. Returns:
 the correlation coefficient of X and Y.

correlationMatrix
public static double[][] correlationMatrix(int[][] data) Computes correlation matrix. Parameters:
data
 The data with random variables in rows and samples in columns. Returns:
 the correlation matrix, M, where M[i][j] is the correlation coefficient of data[i] and data[j].

correlationMatrix
public static double[][] correlationMatrix(double[][] data) Computes correlation matrix. Parameters:
data
 The data with random variables in rows and samples in columns. Returns:
 the correlation matrix, M, where M[i][j] is the correlation coefficient of data[i] and data[j].

tTestUnequalVariances
public static double tTestUnequalVariances(double[] data1, double[] data2) Welch's ttest, also known as ttest with unequal variances. The Welch's ttest can be used when variances are unequal and is also applicable if sample sizes differ. Parameters:
data1
 First dataset.data2
 Second dataset. Returns:
 The t statistic.

tTestUnequalVariances
public static double tTestUnequalVariances(int[] data1, int[] data2) Welch's ttest, also known as ttest with unequal variances. The Welch's ttest can be used when variances are unequal and is also applicable if sample sizes differ. Parameters:
data1
 First dataset.data2
 Second dataset. Returns:
 The t statistic.

tTestWelch
Welch's ttest, also known as ttest with unequal variances. The Welch's ttest can be used when variances are unequal and is also applicable if sample sizes differ. This method computes both the t statistic, as well as the approximate degrees of freedom. Parameters:
data1
 First dataset.data2
 Second dataset. Returns:
 An array, a, of length 2 such that a[0] is the t statistic (as a Double object), and a[1] is the degrees of freedom (as an Integer object).

tTestWelch
Welch's ttest, also known as ttest with unequal variances. The Welch's ttest can be used when variances are unequal and is also applicable if sample sizes differ. This method computes both the t statistic, as well as the approximate degrees of freedom. Parameters:
data1
 First dataset.data2
 Second dataset. Returns:
 An array, a, of length 2 such that a[0] is the t statistic (as a Double object), and a[1] is the degrees of freedom (as an Integer object).

p
public static double p(double t, int dof) Calculates a pvalue from the t statistic and degrees of freedom from a ttest. Parameters:
t
 the t statisticdof
 the degrees of freedom Returns:
 p
 Throws:
ArithmeticException
 if the calculation of the incomplete beta function, required to compute p, fails to converge. The most likely cause if this occurs is excessively high degrees of freedom. However, this is highly unlikely to occur. Our testing has so far failed to cause this exception to occur even with dof as high as 10,000,000.
