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.
Highlights
A multitude of processes in water engineering involve more than one random variable
Comparisons confirmed the appropriateness of the principle of maximum entropy (POME)-based univariate distribution
Using the sample data with the known univariate populations and known dependence (Gumbel–Hougaard), it is concluded that the POME-based distribution derived may model the univariate distribution well
Summary
A multitude of processes in water engineering involve more than one random variable. Droughts are described by their severity, duration, inter-arrival time, and areal extent, which are random. Extreme precipitation events are represented by their intensity, amount, duration, and inter-arrival time, which are all random. Inter-basin water transfer involves transfer of excess water from one basin (say, donor) to a water deficient basin (say, recipient). The transfer involves the volume of water, availability of water in both donor and recipient basins, duration of transfer, rate of transfer, Singh and Zhang Geosci. (2018) 5:6 variables considering the dependence structure among them. Nowadays, these stochastic processes can be modeled with the copula–entropy theory that has proven to be more flexible and accurate than the traditional approaches. The objective of this paper is to reflect on some recent advances made in the application of the copula–entropy theory and future challenges
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