Package org.apache.commons.statistics.descriptive

Class IntStandardDeviation

  • All Implemented Interfaces:
    DoubleSupplier, IntConsumer, IntSupplier, LongSupplier, IntStatistic, StatisticAccumulator<IntStandardDeviation>, StatisticResult
    public final class IntStandardDeviation
extends Object
implements IntStatistic, StatisticAccumulator<IntStandardDeviation>
    Computes the standard deviation of the available values. The default implementation uses the following definition of the sample standard deviation:

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

    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. Omitting the square root, this provides 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. Note however that square root is a concave function and thus introduces negative bias (by Jensen's inequality), which depends on the distribution, and thus the corrected sample standard deviation (using Bessel's correction) is less biased, but still biased.

    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:
    Standard deviation (Wikipedia), Bessel's correction, Jensen's inequality, IntVariance

    • Method Detail

      • create

        public static IntStandardDeviation create()
        Creates an instance.

        The initial result is NaN.

        Returns:
        IntStandardDeviation instance.

      • of

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

      • accept

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

      • getAsDouble

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

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

        Specified by:
        getAsDouble in interface DoubleSupplier
        Returns:
        standard deviation of all values.

      • setBiased

        public IntStandardDeviation setBiased​(boolean v)
        Sets the value of the biased flag. The default value is false. The bias term refers to the computation of the variance; the standard deviation is returned as the square root of the biased or unbiased sample variance. For further details see IntVarianceVariance.setBiased.

        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
        See Also:
        IntVariance.setBiased(boolean)