Estimation of the generalized extreme-value distribution by the method of probability-weighted moments

J. R.M. Hosking; J. R. Wallis; Eric F. Wood

doi:10.1080/00401706.1985.10488049

Estimation of the generalized extreme-value distribution by the method of probability-weighted moments

J. R.M. Hosking
, J. R. Wallis
, Eric F. Wood

Research output: Contribution to journal › Article › peer-review

1105 Scopus citations

Abstract

We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.

Original language	English (US)
Pages (from-to)	251-261
Number of pages	11
Journal	Technometrics
Volume	27
Issue number	3
DOIs	https://doi.org/10.1080/00401706.1985.10488049
State	Published - Aug 1985

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

Generalized extreme-value distribution
Hypothesis testing
Order statistics
Probability-weighted moments

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10.1080/00401706.1985.10488049

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title = "Estimation of the generalized extreme-value distribution by the method of probability-weighted moments",

abstract = "We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.",

keywords = "Generalized extreme-value distribution, Hypothesis testing, Order statistics, Probability-weighted moments",

author = "Hosking, \{J. R.M.\} and Wallis, \{J. R.\} and Wood, \{Eric F.\}",

note = "Funding Information: This cooperative work was supported by the Institute of Hydrology, Wallingford, England. We are greatly indebted to J. S. G. McCulloch (Director of the Institute of Hydrology), P. E. O{\textquoteright}Connell, and R. T. Clarke for initiating and sustaining this research effort. Part of J. R. M. Hosking{\textquoteright}s researchw as carried out at the Mathematics ResearchC enter, University of Wisconsin-Madison, with the support of U.S. Army Contract DAAG29-80-C-0041.",

year = "1985",

month = aug,

doi = "10.1080/00401706.1985.10488049",

language = "English (US)",

volume = "27",

pages = "251--261",

journal = "Technometrics",

issn = "0040-1706",

publisher = "Taylor and Francis Ltd.",

number = "3",

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TY - JOUR

T1 - Estimation of the generalized extreme-value distribution by the method of probability-weighted moments

AU - Hosking, J. R.M.

AU - Wallis, J. R.

AU - Wood, Eric F.

N1 - Funding Information: This cooperative work was supported by the Institute of Hydrology, Wallingford, England. We are greatly indebted to J. S. G. McCulloch (Director of the Institute of Hydrology), P. E. O’Connell, and R. T. Clarke for initiating and sustaining this research effort. Part of J. R. M. Hosking’s researchw as carried out at the Mathematics ResearchC enter, University of Wisconsin-Madison, with the support of U.S. Army Contract DAAG29-80-C-0041.

PY - 1985/8

Y1 - 1985/8

N2 - We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.

AB - We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.

KW - Generalized extreme-value distribution

KW - Hypothesis testing

KW - Order statistics

KW - Probability-weighted moments

UR - https://www.scopus.com/pages/publications/0022113451

UR - https://www.scopus.com/pages/publications/0022113451#tab=citedBy

U2 - 10.1080/00401706.1985.10488049

DO - 10.1080/00401706.1985.10488049

M3 - Article

AN - SCOPUS:0022113451

SN - 0040-1706

VL - 27

SP - 251

EP - 261

JO - Technometrics

JF - Technometrics

IS - 3

ER -

Estimation of the generalized extreme-value distribution by the method of probability-weighted moments

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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