Package org.cicirello.math.stats
Class Statistics
 java.lang.Object

 org.cicirello.math.stats.Statistics

public final class Statistics extends Object
Utility class of basic statistics.


Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static 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
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 Detail

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.

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
public static Number[] tTestWelch(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. 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
public static Number[] tTestWelch(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. 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).

