Package elki.math.statistics.intrinsicdimensionality

Class ZipfEstimator

java.lang.Object

elki.math.statistics.intrinsicdimensionality.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

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	ZipfEstimator.Par	Parameterization class.

Field Summary

Fields

Modifier and Type	Field	Description
static ZipfEstimator	STATIC	Static instance.

Constructor Summary

Constructors

Constructor	Description
ZipfEstimator()

Method Summary

Modifier and Type	Method	Description
<A> double	estimate(A data, NumberArrayAdapter<?,? super A> adapter, int end)	Estimate from a distance list.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface elki.math.statistics.intrinsicdimensionality.DistanceBasedIntrinsicDimensionalityEstimator

estimate, estimate, estimate, estimate, estimate

Field Detail

STATIC

public static final ZipfEstimator STATIC

Static instance.

Constructor Detail

ZipfEstimator

public ZipfEstimator()

Method Detail

estimate

public <A> double estimate(A data,
                           NumberArrayAdapter<?,? super A> adapter,
                           int end)

Description copied from interface: DistanceBasedIntrinsicDimensionalityEstimator

Estimate from a distance list.

Specified by:

estimate in interface DistanceBasedIntrinsicDimensionalityEstimator

Type Parameters:

A - array type

Parameters:

data - Data

adapter - Array adapter

end - Length

Returns:

Estimated intrinsic dimensionality