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

Class ProbabilityWeightedMoments

java.lang.Object

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

@Reference(authors="J. R. M. Hosking, J. R. Wallis, E. F. Wood",title="Estimation of the generalized extreme-value distribution by the method of probability-weighted moments.",booktitle="Technometrics 27.3",url="https://doi.org/10.1080/00401706.1985.10488049",bibkey="doi:10.1080/00401706.1985.10488049") @Reference(authors="J. R. M. Hosking",title="Fortran routines for use with the method of L-moments Version 3.03",booktitle="IBM Research Technical Report",bibkey="tr/ibm/Hosking00")
public final class ProbabilityWeightedMoments
extends java.lang.Object

Estimate the L-Moments of a sample.

Reference:

J. R. M. Hosking, J. R. Wallis, E. F. Wood
Estimation of the generalized extreme-value distribution by the method of probability-weighted moments.
Technometrics 27.3

Also based on:

J. R. M. Hosking
Fortran routines for use with the method of L-moments Version 3.03
IBM Research.

Since:

0.6.0

Author:

Erich Schubert

Constructor Summary

Constructors

Modifier	Constructor and Description
private	ProbabilityWeightedMoments() Private constructor, use static methods!

Method Summary

Modifier and Type	Method and Description
static <A> double[]	alphaBetaPWM(A data, NumberArrayAdapter<?,A> adapter, int nmom) Compute the alpha_r and beta_r factors in parallel using the method of probability-weighted moments.
static <A> double[]	alphaPWM(A data, NumberArrayAdapter<?,A> adapter, int nmom) Compute the alpha_r factors using the method of probability-weighted moments.
static <A> double[]	betaPWM(A data, NumberArrayAdapter<?,A> adapter, int nmom) Compute the beta_r factors using the method of probability-weighted moments.
private static void	normalizeLMR(double[] sum, int nmom) Normalize the moments
static <A> double[]	samLMR(A sorted, NumberArrayAdapter<?,A> adapter, int nmom) Compute the sample L-Moments using probability weighted moments.

Methods inherited from class java.lang.Object

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

Constructor Detail

ProbabilityWeightedMoments

private ProbabilityWeightedMoments()

Private constructor, use static methods!

Method Detail

alphaPWM

public static <A> double[] alphaPWM(A data,
                                    NumberArrayAdapter<?,A> adapter,
                                    int nmom)

Compute the alpha_r factors using the method of probability-weighted moments.

Parameters:

data - Presorted data array.

adapter - Array adapter.

nmom - Number of moments to compute

Returns:

Alpha moments (0-indexed)

betaPWM

public static <A> double[] betaPWM(A data,
                                   NumberArrayAdapter<?,A> adapter,
                                   int nmom)

Compute the beta_r factors using the method of probability-weighted moments.

Parameters:

data - Presorted data array.

adapter - Array adapter.

nmom - Number of moments to compute

Returns:

Beta moments (0-indexed)

alphaBetaPWM

public static <A> double[] alphaBetaPWM(A data,
                                        NumberArrayAdapter<?,A> adapter,
                                        int nmom)

Compute the alpha_r and beta_r factors in parallel using the method of probability-weighted moments. Usually cheaper than computing them separately.

Parameters:

data - Presorted data array.

adapter - Array adapter.

nmom - Number of moments to compute

Returns:

Alpha and Beta moments (0-indexed, interleaved)

samLMR

public static <A> double[] samLMR(A sorted,
                                  NumberArrayAdapter<?,A> adapter,
                                  int nmom)

Compute the sample L-Moments using probability weighted moments.

Parameters:

sorted - Presorted data array.

adapter - Array adapter.

nmom - Number of moments to compute

Returns:

Array containing Lambda1, Lambda2, Tau3 ... TauN

normalizeLMR

private static void normalizeLMR(double[] sum,
                                 int nmom)

Normalize the moments

Parameters:

sum - Sums

nmom - Number of moments