de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality

Class ZipfEstimator

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.AbstractIntrinsicDimensionalityEstimator

de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.ZipfEstimator

All Implemented Interfaces:

IntrinsicDimensionalityEstimator

@Reference(authors="M. Kratz and S. I. Resnick",
           title="On Least Squares Estimates of an Exponential Tail Coefficient",
           booktitle="Statistics & Risk Modeling. Band 14, Heft 4",
           url="http://dx.doi.org/10.1524/strm.1996.14.4.353")
public class ZipfEstimator
extends AbstractIntrinsicDimensionalityEstimator

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 and S. I. Resnick
The QQ-estimator and heavy tails.
Stochastic Models, 12(4), 699-724.

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

J. Beirlant and G. Dierckx and A. Guillou
Estimation of the extreme-value index and generalized quantile plots.
Bernoulli, 11(6), 949-970.

TODO: possible to improve numerical precision via log1p?

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
static ZipfEstimator	STATIC Static instance.

Constructor Summary

Constructors

Constructor and Description
ZipfEstimator()

Method Summary

Methods

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

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.intrinsicdimensionality.AbstractIntrinsicDimensionalityEstimator

estimate, estimate, estimate

Methods inherited from class java.lang.Object

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

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<?,A> adapter,
                  int len)

Description copied from interface: IntrinsicDimensionalityEstimator

Estimate from a distance list.

Type Parameters:

A - array type

Parameters:

data - Data

adapter - Array adapter

len - Length

Returns:

Estimated intrinsic dimensionality