A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis
Abstract The study has investigated the implications of three estimation methods, namely L-moments, Maximum Likelihood, and Maximum Product of Spacing (MPS), for fitting the four-parameter Kappa Distribution (KAPD) in extreme value analysis using Monte Carlo simulations. The accuracy of the estimate...
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Nature Portfolio
2025-01-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-84056-1 |
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| author | Muhammad Shafeeq ul Rehman Khan Zamir Hussain Sadaf Sher Muhammad Amjad Faisal Baig Ishfaq Ahmad Hamd Ullah |
| author_facet | Muhammad Shafeeq ul Rehman Khan Zamir Hussain Sadaf Sher Muhammad Amjad Faisal Baig Ishfaq Ahmad Hamd Ullah |
| author_sort | Muhammad Shafeeq ul Rehman Khan |
| collection | DOAJ |
| description | Abstract The study has investigated the implications of three estimation methods, namely L-moments, Maximum Likelihood, and Maximum Product of Spacing (MPS), for fitting the four-parameter Kappa Distribution (KAPD) in extreme value analysis using Monte Carlo simulations. The accuracy of the estimates has been evaluated using root mean square error (RMSE) and bias. The paper also includes an analysis of the effect of the estimation method on the estimated quantiles considering a real-life example of annual maximum peak flows and the Generalized Normal Distribution as the error distribution. Assessment metrics of the empirical analysis include standard error, L-scale, and 90% confidence limits of the estimated quantiles. The results reveal that MPS is a preferred method of estimation of parameters for KAPD, i.e. having the lowest RMSE values, especially in the presence of heavier tail and significant positive skewness for small to very large sample sizes. Secondly, the method of L-moments is recommended due to its low bias while analyzing the distribution of shape parameters having a slightly heavier tail, and slight or moderate positive skewness. The results associated with the quality of estimated quantiles using real-life data are consistent with the findings of simulation outcomes. |
| format | Article |
| id | doaj-art-5092fa45703b4201bae0bc63e5deedbf |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-5092fa45703b4201bae0bc63e5deedbf2025-08-20T02:46:12ZengNature PortfolioScientific Reports2045-23222025-01-0115111510.1038/s41598-024-84056-1A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysisMuhammad Shafeeq ul Rehman Khan0Zamir Hussain1Sadaf Sher2Muhammad Amjad3Faisal Baig4Ishfaq Ahmad5Hamd Ullah6Department of Civil, Environmental Engineering and Architecture, University of CagliariSchool of Interdisciplinary Engineering and Sciences (SINES), National University of Sciences and Technology (NUST)Center for Advanced Studies in Water, Sadaf Sher U.S, Mehran University of Engineering & TechnologyJoint International Research Laboratory of Environment and Health, Guangdong Provincial Engineering Technology Research Center of Environmental Pollution and Health Risk Assessment, Department of Occupational and Environmental Health, School of Public Health, Muhammad Amjad Postdoctroal Researcher, Ministry of Education, Sun Yat-sen UniversityNational Water and Energy Center, UAE UniversityDepartment of Mathematics and Statistics, International Islamic University IslamabadDepartment of Statistics, Federal Govt. Quaid-i-Azam Degree College, Hamd Ullah, National University of PakistanAbstract The study has investigated the implications of three estimation methods, namely L-moments, Maximum Likelihood, and Maximum Product of Spacing (MPS), for fitting the four-parameter Kappa Distribution (KAPD) in extreme value analysis using Monte Carlo simulations. The accuracy of the estimates has been evaluated using root mean square error (RMSE) and bias. The paper also includes an analysis of the effect of the estimation method on the estimated quantiles considering a real-life example of annual maximum peak flows and the Generalized Normal Distribution as the error distribution. Assessment metrics of the empirical analysis include standard error, L-scale, and 90% confidence limits of the estimated quantiles. The results reveal that MPS is a preferred method of estimation of parameters for KAPD, i.e. having the lowest RMSE values, especially in the presence of heavier tail and significant positive skewness for small to very large sample sizes. Secondly, the method of L-moments is recommended due to its low bias while analyzing the distribution of shape parameters having a slightly heavier tail, and slight or moderate positive skewness. The results associated with the quality of estimated quantiles using real-life data are consistent with the findings of simulation outcomes.https://doi.org/10.1038/s41598-024-84056-1Extreme quantiles, Kappa distributionL-momentsMaximum product of spacingShape parameters |
| spellingShingle | Muhammad Shafeeq ul Rehman Khan Zamir Hussain Sadaf Sher Muhammad Amjad Faisal Baig Ishfaq Ahmad Hamd Ullah A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis Scientific Reports Extreme quantiles, Kappa distribution L-moments Maximum product of spacing Shape parameters |
| title | A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis |
| title_full | A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis |
| title_fullStr | A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis |
| title_full_unstemmed | A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis |
| title_short | A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis |
| title_sort | comparative analysis of l moments maximum likelihood and maximum product of spacing methods for the four parameter kappa distribution in extreme value analysis |
| topic | Extreme quantiles, Kappa distribution L-moments Maximum product of spacing Shape parameters |
| url | https://doi.org/10.1038/s41598-024-84056-1 |
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