Copula–entropy theory for multivariate stochastic modeling in water engineering
Abstract The copula–entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonli...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-02-01
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| Series: | Geoscience Letters |
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| Online Access: | http://link.springer.com/article/10.1186/s40562-018-0105-z |
| _version_ | 1831545261619412992 |
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| author | Vijay P. Singh Lan Zhang |
| author_facet | Vijay P. Singh Lan Zhang |
| author_sort | Vijay P. Singh |
| collection | DOAJ |
| description | Abstract The copula–entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) have been applied to multivariate modeling in water engineering. This study evaluates the copula–entropy theory using a sample dataset with known population information and a flood dataset from the experimental watershed at the Walnut Gulch, Arizona. The study finds the following: (1) both univariate and joint distributions can be derived using the entropy theory. (2) The parametric copula fits the true copula better using empirical marginals than using fitted parametric/entropy-based marginals. This suggests that marginals and copula may be identified separately in which the copula is investigated with empirical marginals. (3) For a given set of constraints, the most entropic canonical copula (MECC) is unique and independent of the marginals. This allows the universal solution for the proposed analysis. (4) The MECC successfully models the joint distribution of bivariate random variables. (5) Using the “AND” case return period analysis as an example, the derived MECC captures the change of return period resulting from different marginals. |
| first_indexed | 2024-12-17T01:24:25Z |
| format | Article |
| id | doaj.art-dc36afbefc2b48c8ad12e8b082b76801 |
| institution | Directory Open Access Journal |
| issn | 2196-4092 |
| language | English |
| last_indexed | 2024-12-17T01:24:25Z |
| publishDate | 2018-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Geoscience Letters |
| spelling | doaj.art-dc36afbefc2b48c8ad12e8b082b768012022-12-21T22:08:44ZengSpringerOpenGeoscience Letters2196-40922018-02-015111710.1186/s40562-018-0105-zCopula–entropy theory for multivariate stochastic modeling in water engineeringVijay P. Singh0Lan Zhang1Department of Biological & Agricultural Engineering, Texas A&M UniversityDepartment of Biological & Agricultural Engineering, Texas A&M UniversityAbstract The copula–entropy theory combines the entropy theory and the copula theory. The entropy theory has been extensively applied to derive the most probable univariate distribution subject to specified constraints by applying the principle of maximum entropy. With the flexibility to model nonlinear dependence structure, parametric copulas (e.g., Archimedean, extreme value, meta-elliptical, etc.) have been applied to multivariate modeling in water engineering. This study evaluates the copula–entropy theory using a sample dataset with known population information and a flood dataset from the experimental watershed at the Walnut Gulch, Arizona. The study finds the following: (1) both univariate and joint distributions can be derived using the entropy theory. (2) The parametric copula fits the true copula better using empirical marginals than using fitted parametric/entropy-based marginals. This suggests that marginals and copula may be identified separately in which the copula is investigated with empirical marginals. (3) For a given set of constraints, the most entropic canonical copula (MECC) is unique and independent of the marginals. This allows the universal solution for the proposed analysis. (4) The MECC successfully models the joint distribution of bivariate random variables. (5) Using the “AND” case return period analysis as an example, the derived MECC captures the change of return period resulting from different marginals.http://link.springer.com/article/10.1186/s40562-018-0105-zCopula theoryEntropy theoryMultivariate stochastic modelingProbability density functionMost entropic canonical copulaReturn period |
| spellingShingle | Vijay P. Singh Lan Zhang Copula–entropy theory for multivariate stochastic modeling in water engineering Geoscience Letters Copula theory Entropy theory Multivariate stochastic modeling Probability density function Most entropic canonical copula Return period |
| title | Copula–entropy theory for multivariate stochastic modeling in water engineering |
| title_full | Copula–entropy theory for multivariate stochastic modeling in water engineering |
| title_fullStr | Copula–entropy theory for multivariate stochastic modeling in water engineering |
| title_full_unstemmed | Copula–entropy theory for multivariate stochastic modeling in water engineering |
| title_short | Copula–entropy theory for multivariate stochastic modeling in water engineering |
| title_sort | copula entropy theory for multivariate stochastic modeling in water engineering |
| topic | Copula theory Entropy theory Multivariate stochastic modeling Probability density function Most entropic canonical copula Return period |
| url | http://link.springer.com/article/10.1186/s40562-018-0105-z |
| work_keys_str_mv | AT vijaypsingh copulaentropytheoryformultivariatestochasticmodelinginwaterengineering AT lanzhang copulaentropytheoryformultivariatestochasticmodelinginwaterengineering |