Statistical characteristics of earthquake magnitude based on the composite model
Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribut...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024032?viewType=HTML |
| _version_ | 1827385903973138432 |
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| author | Yanfang Zhang Fuchang Wang Yibin Zhao |
| author_facet | Yanfang Zhang Fuchang Wang Yibin Zhao |
| author_sort | Yanfang Zhang |
| collection | DOAJ |
| description | Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis. |
| first_indexed | 2024-03-08T15:34:18Z |
| format | Article |
| id | doaj.art-2f68e5def2284def8d44c5b1e9d9225d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T15:34:18Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-2f68e5def2284def8d44c5b1e9d9225d2024-01-10T01:16:02ZengAIMS PressAIMS Mathematics2473-69882024-01-019160762410.3934/math.2024032Statistical characteristics of earthquake magnitude based on the composite modelYanfang Zhang 0Fuchang Wang1Yibin Zhao2Department of Mathematics, Institute of Disaster Prevention, No. 465, Xueyuan Street, Yanjiao High Tech Zone, Sanhe City, Hebei Province, 065201, ChinaDepartment of Mathematics, Institute of Disaster Prevention, No. 465, Xueyuan Street, Yanjiao High Tech Zone, Sanhe City, Hebei Province, 065201, ChinaDepartment of Mathematics, Institute of Disaster Prevention, No. 465, Xueyuan Street, Yanjiao High Tech Zone, Sanhe City, Hebei Province, 065201, ChinaThreshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis.https://www.aimspress.com/article/doi/10.3934/math.2024032?viewType=HTMLgeneralized pareto distributioncomposite modelempirical distribution functionseismic hazard |
| spellingShingle | Yanfang Zhang Fuchang Wang Yibin Zhao Statistical characteristics of earthquake magnitude based on the composite model AIMS Mathematics generalized pareto distribution composite model empirical distribution function seismic hazard |
| title | Statistical characteristics of earthquake magnitude based on the composite model |
| title_full | Statistical characteristics of earthquake magnitude based on the composite model |
| title_fullStr | Statistical characteristics of earthquake magnitude based on the composite model |
| title_full_unstemmed | Statistical characteristics of earthquake magnitude based on the composite model |
| title_short | Statistical characteristics of earthquake magnitude based on the composite model |
| title_sort | statistical characteristics of earthquake magnitude based on the composite model |
| topic | generalized pareto distribution composite model empirical distribution function seismic hazard |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024032?viewType=HTML |
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