Class ZipfEstimator

  • All Implemented Interfaces:
    DistanceBasedIntrinsicDimensionalityEstimator, IntrinsicDimensionalityEstimator<java.lang.Object>

    @Reference(authors="M. Kratz, S. I. Resnick",title="The QQ-estimator and heavy tails",booktitle="Communications in Statistics. Stochastic Models 12(4)",url="https://doi.org/10.1080/15326349608807407",bibkey="doi:10.1080/15326349608807407") @Reference(authors="J. Schultze, J. Steinebach",title="On Least Squares Estimates of an Exponential Tail Coefficient",booktitle="Statistics & Risk Modeling 14(4)",url="https://doi.org/10.1524/strm.1996.14.4.353",bibkey="doi:10.1524/strm.1996.14.4.353") @Reference(authors="J. Beirlant, G. Dierckx, A. Guillou",title="Estimation of the extreme-value index and generalized quantile plots",booktitle="Bernoulli 11(6)",url="https://doi.org/10.3150/bj/1137421635",bibkey="doi:10.3150/bj/1137421635")
    public class ZipfEstimator
    extends java.lang.Object
    implements DistanceBasedIntrinsicDimensionalityEstimator
    Zipf estimator (qq-estimator) of the intrinsic dimensionality.

    Unfortunately, this estimator appears to have a bias. We have empirically modified the plot position such that bias is reduced, but could not find the proper way of removing this bias for small samples.

    References:

    M. Kratz, S. I. Resnick
    The QQ-estimator and heavy tails
    Communications in Statistics. Stochastic Models 12(4)

    J. Schultze, J. Steinebach
    On Least Squares Estimates of an Exponential Tail Coefficient
    Statistics and Risk Modeling 14(4)

    J. Beirlant, G. Dierckx, A. Guillou
    Estimation of the extreme-value index and generalized quantile plots
    Bernoulli 11(6)

    Since:
    0.7.0
    Author:
    Erich Schubert