Muhammad Aslam Mohd Safari, N. Masseran, Mohd Azmi Haron
{"title":"Examining Tail Index Estimators in New Pareto Distribution: Monte Carlo Simulations and Income Data Applications","authors":"Muhammad Aslam Mohd Safari, N. Masseran, Mohd Azmi Haron","doi":"10.17576/jsm-2024-5302-18","DOIUrl":null,"url":null,"abstract":"An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum likelihood, method of moments, maximum product of spacing, its modified version, ordinary least squares, weighted least squares, percentile, Kolmogorov-Smirnov, Anderson-Darling, its modified version, Cramér-von Mises, and Zhang's variants of the previous three. Using Monte Carlo simulations, the effectiveness of these estimators is compared both with and without the presence of outliers. The findings show that, without outliers, the maximum product of spacing, its modified version, and maximum likelihood are the most effective estimators. In contrast, with outliers present, the top performers are Cramér-von Mises, ordinary least squares, and weighted least squares. The study further introduces a graphical method called the new Pareto-type quantile plot for validating the new Pareto-type assumptions and outlines a stepwise process to identify the optimal threshold for this distribution. Concluding the study, the new Pareto-type distribution is employed to model the high-end household income data from Italy and Malaysia, leveraging all the methodologies proposed.","PeriodicalId":21366,"journal":{"name":"Sains Malaysiana","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sains Malaysiana","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.17576/jsm-2024-5302-18","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum likelihood, method of moments, maximum product of spacing, its modified version, ordinary least squares, weighted least squares, percentile, Kolmogorov-Smirnov, Anderson-Darling, its modified version, Cramér-von Mises, and Zhang's variants of the previous three. Using Monte Carlo simulations, the effectiveness of these estimators is compared both with and without the presence of outliers. The findings show that, without outliers, the maximum product of spacing, its modified version, and maximum likelihood are the most effective estimators. In contrast, with outliers present, the top performers are Cramér-von Mises, ordinary least squares, and weighted least squares. The study further introduces a graphical method called the new Pareto-type quantile plot for validating the new Pareto-type assumptions and outlines a stepwise process to identify the optimal threshold for this distribution. Concluding the study, the new Pareto-type distribution is employed to model the high-end household income data from Italy and Malaysia, leveraging all the methodologies proposed.
期刊介绍:
Sains Malaysiana is a refereed journal committed to the advancement of scholarly knowledge and research findings of the several branches of science and technology. It contains articles on Earth Sciences, Health Sciences, Life Sciences, Mathematical Sciences and Physical Sciences. The journal publishes articles, reviews, and research notes whose content and approach are of interest to a wide range of scholars. Sains Malaysiana is published by the UKM Press an its autonomous Editorial Board are drawn from the Faculty of Science and Technology, Universiti Kebangsaan Malaysia. In addition, distinguished scholars from local and foreign universities are appointed to serve as advisory board members and referees.