Documentation API of the 'org.apache.commons.math3.stat.descriptive.moment.Variance' Java class

Class Variance

  • All Implemented Interfaces:
    Serializable, StorelessUnivariateStatistic, UnivariateStatistic, WeightedEvaluation, MathArrays.Function

    public class Varianceextends AbstractStorelessUnivariateStatisticimplements Serializable, WeightedEvaluation
    Computes the variance of the available values. By default, the unbiased "sample variance" definitional formula is used:

    variance = sum((x_i - mean)^2) / (n - 1)

    where mean is the Mean and n is the number of sample observations.

    The definitional formula does not have good numerical properties, so this implementation does not compute the statistic using the definitional formula.

    • The getResult method computes the variance using updating formulas based on West's algorithm, as described in Chan, T. F. and J. G. Lewis 1979, Communications of the ACM, vol. 22 no. 9, pp. 526-531.
    • The evaluate methods leverage the fact that they have the full array of values in memory to execute a two-pass algorithm. Specifically, these methods use the "corrected two-pass algorithm" from Chan, Golub, Levesque, Algorithms for Computing the Sample Variance, American Statistician, vol. 37, no. 3 (1983) pp. 242-247.
    Note that adding values using increment or incrementAll and then executing getResult will sometimes give a different, less accurate, result than executing evaluate with the full array of values. The former approach should only be used when the full array of values is not available.

    The "population variance" ( sum((x_i - mean)^2) / n ) can also be computed using this statistic. The isBiasCorrected property determines whether the "population" or "sample" value is returned by the evaluate and getResult methods. To compute population variances, set this property to false.

    Note that this implementation is not synchronized. If multiple threads access an instance of this class concurrently, and at least one of the threads invokes the increment() or clear() method, it must be synchronized externally.

    See Also:
    Serialized Form

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