Class IntVariance

  • All Implemented Interfaces:
    java.util.function.DoubleSupplier, java.util.function.IntConsumer, java.util.function.IntSupplier, java.util.function.LongSupplier, IntStatistic, StatisticAccumulator<IntVariance>, StatisticResult

    public final class IntVariance
    extends java.lang.Object
    implements IntStatistic, StatisticAccumulator<IntVariance>
    Computes the variance of the available values. The default implementation uses the following definition of the sample variance:

    \[ \tfrac{1}{n-1} \sum_{i=1}^n (x_i-\overline{x})^2 \]

    where \( \overline{x} \) is the sample mean, and \( n \) is the number of samples.

    • The result is NaN if no values are added.
    • The result is zero if there is one value in the data set.

    The use of the term \( n − 1 \) is called Bessel's correction. This is an unbiased estimator of the variance of a hypothetical infinite population. If the biased option is enabled the normalisation factor is changed to \( \frac{1}{n} \) for a biased estimator of the sample variance.

    The implementation uses an exact integer sum to compute the scaled (by \( n \)) sum of squared deviations from the mean; this is normalised by the scaled correction factor.

    \[ \frac {n \times \sum_{i=1}^n x_i^2 - (\sum_{i=1}^n x_i)^2}{n \times (n - 1)} \]

    Supports up to 263 (exclusive) observations. This implementation does not check for overflow of the count.

    This class is designed to work with (though does not require) streams.

    This implementation is not thread safe. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the accept or combine method, it must be synchronized externally.

    However, it is safe to use accept and combine as accumulator and combiner functions of Collector on a parallel stream, because the parallel implementation of Stream.collect() provides the necessary partitioning, isolation, and merging of results for safe and efficient parallel execution.

    Since:
    1.1
    See Also:
    variance (Wikipedia), Algorithms for computing the variance (Wikipedia), Bessel's correction
    • Field Summary

      Fields 
      Modifier and Type Field Description
      private boolean biased
      Flag to control if the statistic is biased, or should use a bias correction.
      private long n
      Count of values that have been added.
      (package private) static int SMALL_SAMPLE
      Small array sample size.
      private Int128 sum
      Sum of the values.
      private UInt128 sumSq
      Sum of the squared values.
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private IntVariance()
      Create an instance.
      private IntVariance​(UInt128 sumSq, Int128 sum, int n)
      Create an instance.
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      void accept​(int value)
      Updates the state of the statistic to reflect the addition of value.
      IntVariance combine​(IntVariance other)
      Combines the state of the other statistic into this one.
      (package private) double computeMean()
      Compute the mean.
      private static double computeSSDevN​(UInt128 sumSq, Int128 sum, long n)
      Compute the sum-of-squared deviations multiplied by the count of values: n * sum(x^2) - sum(x)^2.
      (package private) double computeSumOfSquaredDeviations()
      Compute the sum of the squared deviations from the mean.
      (package private) static double computeVarianceOrStd​(UInt128 sumSq, Int128 sum, long n, boolean biased, boolean std)
      Compute the variance (or standard deviation).
      static IntVariance create()
      Creates an instance.
      double getAsDouble()
      Gets the variance of all input values.
      static IntVariance of​(int... values)
      Returns an instance populated using the input values.
      IntVariance setBiased​(boolean v)
      Sets the value of the biased flag.
      private static java.math.BigInteger square​(java.math.BigInteger x)
      Convenience method to square a BigInteger.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
      • Methods inherited from interface java.util.function.IntConsumer

        andThen
    • Field Detail

      • SMALL_SAMPLE

        static final int SMALL_SAMPLE
        Small array sample size. Used to avoid computing with UInt96 then converting to UInt128.
        See Also:
        Constant Field Values
      • sumSq

        private final UInt128 sumSq
        Sum of the squared values.
      • sum

        private final Int128 sum
        Sum of the values.
      • n

        private long n
        Count of values that have been added.
      • biased

        private boolean biased
        Flag to control if the statistic is biased, or should use a bias correction.
    • Constructor Detail

      • IntVariance

        private IntVariance()
        Create an instance.
      • IntVariance

        private IntVariance​(UInt128 sumSq,
                            Int128 sum,
                            int n)
        Create an instance.
        Parameters:
        sumSq - Sum of the squared values.
        sum - Sum of the values.
        n - Count of values that have been added.
    • Method Detail

      • create

        public static IntVariance create()
        Creates an instance.

        The initial result is NaN.

        Returns:
        IntVariance instance.
      • of

        public static IntVariance of​(int... values)
        Returns an instance populated using the input values.
        Parameters:
        values - Values.
        Returns:
        IntVariance instance.
      • accept

        public void accept​(int value)
        Updates the state of the statistic to reflect the addition of value.
        Specified by:
        accept in interface java.util.function.IntConsumer
        Parameters:
        value - Value.
      • getAsDouble

        public double getAsDouble()
        Gets the variance of all input values.

        When no values have been added, the result is NaN.

        Specified by:
        getAsDouble in interface java.util.function.DoubleSupplier
        Returns:
        variance of all values.
      • computeVarianceOrStd

        static double computeVarianceOrStd​(UInt128 sumSq,
                                           Int128 sum,
                                           long n,
                                           boolean biased,
                                           boolean std)
        Compute the variance (or standard deviation).

        The std flag controls if the result is returned as the standard deviation using the square root function.

        Parameters:
        sumSq - Sum of the squared values.
        sum - Sum of the values.
        n - Count of values that have been added.
        biased - Flag to control if the statistic is biased, or should use a bias correction.
        std - Flag to control if the statistic is the standard deviation.
        Returns:
        the variance (or standard deviation)
      • computeSSDevN

        private static double computeSSDevN​(UInt128 sumSq,
                                            Int128 sum,
                                            long n)
        Compute the sum-of-squared deviations multiplied by the count of values: n * sum(x^2) - sum(x)^2.
        Parameters:
        sumSq - Sum of the squared values.
        sum - Sum of the values.
        n - Count of values that have been added.
        Returns:
        the sum-of-squared deviations precursor
      • computeSumOfSquaredDeviations

        double computeSumOfSquaredDeviations()
        Compute the sum of the squared deviations from the mean.

        This is a helper method used in higher order moments.

        Returns:
        the sum of the squared deviations
      • computeMean

        double computeMean()
        Compute the mean.

        This is a helper method used in higher order moments.

        Returns:
        the mean
      • square

        private static java.math.BigInteger square​(java.math.BigInteger x)
        Convenience method to square a BigInteger.
        Parameters:
        x - Value
        Returns:
        x^2
      • setBiased

        public IntVariance setBiased​(boolean v)
        Sets the value of the biased flag. The default value is false.

        If false the sum of squared deviations from the sample mean is normalised by n - 1 where n is the number of samples. This is Bessel's correction for an unbiased estimator of the variance of a hypothetical infinite population.

        If true the sum of squared deviations is normalised by the number of samples n.

        Note: This option only applies when n > 1. The variance of n = 1 is always 0.

        This flag only controls the final computation of the statistic. The value of this flag will not affect compatibility between instances during a combine operation.

        Parameters:
        v - Value.
        Returns:
        this instance