Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation

GMM estimation of a maximum entropy distribution with interval data

We develop a generalized method of moments (GMM) estimator for the distribution of a variable where summary statistics are available only for intervals of the random variable. Without individual data, one cannot calculate the weighting matrix for the GMM estimator. Instead, we propose a simulated weighting matrix based on a first-step consistent estimate. When the functional form of the underly...

Estimation Using Bivariate Extreme Ranked Set Sampling With Application To The Bivariate Normal Distribution

Maximum Entropy Distribution Estimation with Generalized Regularization

We present a unified and complete account of maximum entropy distribution estimation subject to constraints represented by convex potential functions or, alternatively, by convex regularization. We provide fully general performance guarantees and an algorithm with a complete convergence proof. As special cases, we can easily derive performance guarantees for many known regularization types, inc...

Maximum Entropy-Copula Method for Hydrological Risk Analysis under Uncertainty: A Case Study on the Loess Plateau, China

Copula functions have been extensively used to describe the joint behaviors of extreme hydrological events and to analyze hydrological risk. Advanced marginal distribution inference, for example, the maximum entropy theory, is particularly beneficial for improving the performance of the copulas. The goal of this paper, therefore, is twofold; first, to develop a coupled maximum entropy-copula me...

Bivariate Rainfall and Runoff Analysis Using Entropy and Copula Theories

Multivariate hydrologic frequency analysis has been widely studied using: (1) commonly known joint distributions or copula functions with the assumption of univariate variables being independently identically distributed (I.I.D.) random variables; or (2) directly applying the entropy theory-based framework. However, for the I.I.D. univariate random variable assumption, the univariate variable m...