{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T04:20:00Z","timestamp":1769919600677,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T00:00:00Z","timestamp":1710720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Office for Philosophy and Social Sciences","award":["20BTJ054"],"award-info":[{"award-number":["20BTJ054"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions.<\/jats:p>","DOI":"10.3390\/sym16030365","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T06:58:39Z","timestamp":1710745119000},"page":"365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model"],"prefix":"10.3390","volume":"16","author":[{"given":"Wenru","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Xu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}]},{"given":"Mi","family":"Zhou","sequence":"additional","affiliation":[{"name":"China National Environmental Monitoring Center, Beijing 100012, China"}]},{"given":"Haiqing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Economics, Nanjing University of Finance and Economics, Nanjing 210023, China"}]},{"given":"Qingqing","family":"Ji","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"Weihu","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1093\/biomet\/75.3.397","article-title":"Bivariate extreme value theory: Models and estimation","volume":"75","author":"Tawn","year":"1988","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1093\/biomet\/77.2.245","article-title":"Modelling multivariate extreme value distributions","volume":"77","author":"Tawn","year":"1988","journal-title":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1080\/10920277.1999.10595797","article-title":"Extreme Value Theory as a Risk Management Tool","volume":"3","author":"Embrechts","year":"1999","journal-title":"N. Am. Actuar. J."},{"key":"ref_4","first-page":"119","article-title":"Statistical inference using extreme order statistics","volume":"3","author":"Pickands","year":"1975","journal-title":"Ann. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1080\/00401706.1987.10488243","article-title":"Parameter and quantile estimation for the generalized pareto distribution","volume":"29","author":"Hosking","year":"1987","journal-title":"Technometrics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1029\/WR015i005p01049","article-title":"Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form","volume":"15","author":"Greenwood","year":"1979","journal-title":"Water Resour. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1093\/biomet\/72.1.67","article-title":"Maximum likelihood estimation in a class of nonregular cases","volume":"72","author":"Smith","year":"1985","journal-title":"Biometrika"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/0022-1694(93)90160-B","article-title":"A comparative study for the estimators of the generalized pareto distribution","volume":"150","author":"Moharram","year":"1993","journal-title":"J. Hydrol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1111\/j.2517-6161.1990.tb01775.x","article-title":"L-moments: Analysis and estimation of distributions using linear combinations of order statistics","volume":"52","author":"Hosking","year":"1990","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0022-1694(95)02793-9","article-title":"On some methods of fitting the generalized pareto distributions","volume":"177","author":"Ashkar","year":"1996","journal-title":"J. Hydrol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1080\/01621459.1997.10473683","article-title":"Fitting the generalized pareto distribution to data","volume":"92","author":"Castillo","year":"1997","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1007\/s10651-022-00548-1","article-title":"Some efficient closed-form estimators of the parameters of the generalized pareto distribution","volume":"29","author":"From","year":"2022","journal-title":"Environ. Ecol. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1029\/2001WR900014","article-title":"Generalized probability weighted moments: Application to the generalized pareto distribution","volume":"37","author":"Rasmussen","year":"2001","journal-title":"Water Resour. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/j.1467-842X.2006.00464.x","article-title":"Likelihood moment estimation for the generalized pareto distribution","volume":"49","author":"Zhang","year":"2007","journal-title":"Aust. N. Z. J. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1198\/tech.2009.08017","article-title":"A new and efficient estimation method for the generalized pareto distribution","volume":"51","author":"Zhang","year":"2009","journal-title":"Technometrics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.csda.2011.06.030","article-title":"A quantile estimation for massive data with generalized pareto distribution","volume":"56","author":"Song","year":"2012","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.csda.2015.12.008","article-title":"Estimating extreme tail risk measures with generalized pareto distribution","volume":"98","author":"Park","year":"2016","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7761","DOI":"10.1080\/03610918.2016.1249884","article-title":"Parameter estimation for generalized Pareto distribution by generalized probability weighted moment-equations","volume":"46","author":"Chen","year":"2017","journal-title":"Commun.-Stat.-Simul. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1080\/00401706.2016.1270857","article-title":"Minimum distance estimation for the generalized pareto distribution","volume":"59","author":"Chen","year":"2017","journal-title":"Technometrics"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mart\u00edn, J., Parra, M.I., Pizarro, M.M., and Sanju\u00e1n, E.L. (2022). Baseline methods for the parameter estimation of the generalized pareto distribution. Entropy, 24.","DOI":"10.3390\/e24020178"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2659","DOI":"10.1002\/2015WR018502","article-title":"Threshold detection for the generalized pareto distribution: Review of representative methods and application to the noaa ncdc daily rainfall database","volume":"52","author":"Langousis","year":"2016","journal-title":"Water Resour. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1198\/00401700152672573","article-title":"Goodness-of-fit tests for the generalized pareto distribution","volume":"43","author":"Choulakian","year":"2001","journal-title":"Technometricsh"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1111\/rssb.12122","article-title":"Sequential selection procedures and false discovery rate control","volume":"78","author":"Wager","year":"2016","journal-title":"J. R. Stat. Ser. B Stat. Methodol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1214\/17-AOAS1092","article-title":"Automated threshold selection for extreme value analysis via ordered goodness-of-fit tests with adjustment for false discovery rate","volume":"12","author":"Bader","year":"2018","journal-title":"Ann. Appl. Stat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1550147718757698","article-title":"Threshold selection for extreme value estimation of vehicle load effect on bridges","volume":"14","author":"Yang","year":"2018","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s40998-018-0160-7","article-title":"A new threshold selection method based on fuzzy expert systems for separating text from the background of document images","volume":"43","author":"Annabestani","year":"2019","journal-title":"Iran. J. Sci. Technol. Trans. Electrical Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124845","DOI":"10.1016\/j.jhydrol.2020.124845","article-title":"An evaluation of automated GPD threshold selection methods for hydrological extremes across different scales","volume":"585","author":"Curceac","year":"2020","journal-title":"J. Hydrol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s00477-020-01789-x","article-title":"L-moments for automatic threshold selection in extreme value analysis","volume":"34","year":"2020","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1214\/aop\/1176996548","article-title":"Residual life time at great age","volume":"2","author":"Balkema","year":"1974","journal-title":"Ann. Probab."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.jspi.2008.11.019","article-title":"Parameter estimation of the generalized Pareto distribution\u2014Part I","volume":"140","author":"Kotz","year":"2010","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1029\/WR015i006p01361","article-title":"Estimation of parameters and quantiles of wakeby distributions","volume":"15","author":"Landwehr","year":"1979","journal-title":"Water Resour. Res."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/3\/365\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:15:24Z","timestamp":1760105724000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/3\/365"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,18]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["sym16030365"],"URL":"https:\/\/doi.org\/10.3390\/sym16030365","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,18]]}}}