Statistics (JavaPermutationTools - A Java API for computation on permutations)

java.lang.Object
- org.cicirello.math.stats.Statistics

public final class Statistics
extends Object

Utility class of basic statistics.

Since:: 1.0

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and 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 t-test, also known as t-test with unequal variances.
`static double`	`tTestUnequalVariances(int[] data1, int[] data2)` Welch's t-test, also known as t-test with unequal variances.
`static Number[]`	`tTestWelch(double[] data1, double[] data2)` Welch's t-test, also known as t-test with unequal variances.
`static Number[]`	`tTestWelch(int[] data1, int[] data2)` Welch's t-test, also known as t-test 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.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- 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 t-test, also known as t-test with unequal variances. The Welch's t-test 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.
    
    Since:
    
    1.4
  - tTestUnequalVariances
```
public static double tTestUnequalVariances(int[] data1,
                                           int[] data2)
```
    Welch's t-test, also known as t-test with unequal variances. The Welch's t-test 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.
    
    Since:
    
    1.4
  - tTestWelch
```
public static Number[] tTestWelch(double[] data1,
                                  double[] data2)
```
    Welch's t-test, also known as t-test with unequal variances. The Welch's t-test 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).
    
    Since:
    
    1.4
  - tTestWelch
```
public static Number[] tTestWelch(int[] data1,
                                  int[] data2)
```
    Welch's t-test, also known as t-test with unequal variances. The Welch's t-test 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).
    
    Since:
    
    1.4

Class Statistics

Method Summary

Methods inherited from class java.lang.Object

Method Detail

mean

mean

variance

variance

varianceSample

varianceSample

covariance

covariance

correlation

correlation

correlationMatrix

correlationMatrix

tTestUnequalVariances

tTestUnequalVariances

tTestWelch

tTestWelch