Copula–entropy theory for multivariate stochastic modeling in water engineering View Full Text


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Article Info

DATE

2018-12

AUTHORS

Vijay P. Singh, Lan Zhang

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. More... »

PAGES

6

References to SciGraph publications

  • 1988-07. Possible generalization of Boltzmann-Gibbs statistics in JOURNAL OF STATISTICAL PHYSICS
  • 2016-05. Extension of observed flood series by combining a distributed hydro-meteorological model and a copula-based model in STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
  • 1998. Entropy-Based Parameter Estimation in Hydrology in NONE
  • 2010-03. Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data in STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
  • 2010-05-25. Extreme-Value Copulas in COPULA THEORY AND ITS APPLICATIONS
  • 2016-12. Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas in STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
  • Journal

    TITLE

    Geoscience Letters

    ISSUE

    1

    VOLUME

    5

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s40562-018-0105-z

    DOI

    http://dx.doi.org/10.1186/s40562-018-0105-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1101204447


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