Class LongVariance

java.lang.Object
org.apache.commons.statistics.descriptive.LongVariance
All Implemented Interfaces:
DoubleSupplier, IntSupplier, LongConsumer, LongSupplier, LongStatistic, StatisticAccumulator<LongVariance>, StatisticResult
public final class LongVariance extends Object implements LongStatistic, StatisticAccumulator<LongVariance>
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:

  • Field Details

    • sumSq

      private final UInt192 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 Details

    • LongVariance

      private LongVariance()
      Create an instance.

    • LongVariance

      private LongVariance(UInt192 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 Details

    • create

      public static LongVariance create()
      Creates an instance.

      The initial result is NaN.

      Returns:
      LongVariance instance.

    • of

      public static LongVariance of(long... values)
      Returns an instance populated using the input values.
      Parameters:
      values - Values.
      Returns:
      LongVariance instance.

    • ofRange

      public static LongVariance ofRange(long[] values, int from, int to)
      Returns an instance populated using the specified range of values.
      Parameters:
      values - Values.
      from - Inclusive start of the range.
      to - Exclusive end of the range.
      Returns:
      LongVariance instance.
      Throws:
      IndexOutOfBoundsException - if the sub-range is out of bounds
      Since:
      1.2

    • createFromRange

      static LongVariance createFromRange(long[] values, int from, int to)
      Create an instance using the specified range of values.

      Warning: No range checks are performed.

      Parameters:
      values - Values.
      from - Inclusive start of the range.
      to - Exclusive end of the range.
      Returns:
      LongVariance instance.

    • accept

      public void accept(long value)
      Updates the state of the statistic to reflect the addition of value.
      Specified by:
      accept in interface LongConsumer
      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 DoubleSupplier
      Returns:
      variance of all values.

    • computeVarianceOrStd

      static double computeVarianceOrStd(UInt192 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(UInt192 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 BigInteger square(BigInteger x)
      Convenience method to square a BigInteger.
      Parameters:
      x - Value
      Returns:
      x^2

    • combine

      public LongVariance combine(LongVariance other)
      Description copied from interface: StatisticAccumulator
      Combines the state of the other statistic into this one.
      Specified by:
      combine in interface StatisticAccumulator<LongVariance>
      Parameters:
      other - Another statistic to be combined.
      Returns:
      this instance after combining other.

    • setBiased

      public LongVariance 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