Module org.cicirello.rho_mu
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

    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
    p(double t, int dof)
    Calculates a p-value from the t statistic and degrees of freedom from a t-test.
    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 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 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 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.

    • 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.

    • 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).

    • 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).

    • p

      public static double p(double t, int dof)
      Calculates a p-value from the t statistic and degrees of freedom from a t-test.
      Parameters:
      t - the t statistic
      dof - 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.