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Assessing the joint dependence of air-water temperature and discharge-water temperature in the middle reach of Yangtze River using POME-copula
Published in Chongfu Huang, Zoe Nivolianitou, Risk Analysis Based on Data and Crisis Response Beyond Knowledge, 2019
Yuwei Tao, Yuankun Wang, Dong Wang
Many varying sophisticated approaches have been developed to model different aspects of thermal behavior in space and in time and estimate the effect of dam constructions on water temperature. These have included empirical models that rely on statistical analysis to make predictions from weather data or information on catchment characteristics (Benyahya et al., 2007), the use of wavelet analysis to quantify the effect of multi-purpose dams in decreasing water temperature variability at multiple time scales from 1 to 8 days (Steel and Lange, 2007). Little attention has been paid to explore the dependence structures among water temperature and factors (e.g. air temperature and discharge) from a probabilistic perspective. Copulas provide a useful tool for exploring this type of problem. A copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform; it describes the dependence structure among the marginal distributions of the individual variables (Liu et al., 2017). Copulas have been increasingly used in hydrometeorological multivariate applications including frequency analysis, dependence analysis and risk analysis regarding extreme conditions. To develop a flexible, unbiased statistical inference framework, the principle of maximum entropy (POME) is being increasingly coupled with copula (Liu et al., 2017). POME is to derive the marginal distribution for copula, best capturing the shape of probability density function.
Models and Modelling
Published in Shyama Prasad Mukherjee, A Guide to Research Methodology, 2019
An interesting application of copulas is in risk management, where risks correspond to right tails of loss distributions. In a portfolio of investments, large losses are often caused by simultaneous large moves in several components. Thus a consideration of simultaneous extremes becomes important and is facilitated by the copula. The lower tail dependence of Xi and Xj is given by λ = lim Pr [Xi ≤ Fi−1 (u) | Xj ≤ Fj−1 (u)] as u tends to zero
Copula Functions and Drought
Published in Saeid Eslamian, Faezeh Eslamian, Handbook of Drought and Water Scarcity, 2017
Shahrbanou Madadgar, Hamid Moradkhani
While a number of studies have focused on accurate characterization of future droughts, work is still required on the forecast methods to identify the probabilistic features of future droughts. Most of the currently available methods are unable to estimate the full probability distribution of droughts. Developing the conditional probability of a drought status in the future, given the observed status in the past, requires advanced methodologies to address the connections and dependencies between drought events. For this purpose, a group of powerful statistical functions, called copula functions, has been recently utilized to establish drought forecasting models with substantial probabilistic features [60,62,87]. Copulas are multivariate distribution functions that join the random variables with some level of correlation and dependency. Since there are a lot of correlated variables in hydrologic applications, copula functions have been extensively used in the modeling of various hydrologic phenomena, including flood analyses (e.g., [24,96,121]), rainfall and runoff analyses [28,44,95,122], spatial analysis of groundwater quality parameters [3,4], and synthesizing and downscaling of monthly river flow [53]. In another recent study, copulas contributed to the postprocessing of hydrologic forecasts [61] and were found to be a robust alternative for reducing the uncertainty and increasing the reliability of hydrologic forecasts. In low-flow and drought analyses, copulas have been employed to characterize drought events according to the dependent structure between droughts’ severity, intensity, and duration [21,45,59,103,119]. Recently, Madadgar and Moradkhani [60,62] introduced a new application of copula functions, where they defined a copula-based forecast model and studied the probabilistic features of seasonal droughts.
A Practical Approach of Probabilistic Seismic Hazard Analysis for Vector IMs Regarding Mainshock with Potentially Largest Aftershock
Published in Journal of Earthquake Engineering, 2023
Xiao-Hui Yu, Zhou Zhou, Da-Gang Lu, Kun Ji
Figure 1 illustrates the copula-based seismic hazard analysis approach for mainshock with potentially largest aftershock. The proposed approach can be divided into two main components: 1) the standard PSHA for mainshock to calculate MAR(IMMS); and 2) the copula-based development of the joint probability distribution between IMMS and IMAS to calculate P[IMAS|IMMS]. The standard PSHA procedures are well known and are not described herein. For the development of the joint distribution of IMMS and IMAS, a copula function should be used to couple the marginal distributions of both IMMS and IMAS together (see Eq. 10). During the past years, a variety of copula functions have been developed, which can be generally categorized into several families (Durante and Sempi 2010; Nelsen 2007; Phoon and Ching 2015), i.e. Elliptical copulas, Archimedean copulas, and Plackett copulas, etc. Different types of copula functions would lead to different dependence features, e.g. light or heavy tail, and symmetries or asymmetries. Therefore, an optimal copula function should be selected first from the alternatives by best capturing the dependence features of the data.
Modeling travel time volatility using copula-based Monte Carlo simulation method for probabilistic traffic prediction
Published in Transportmetrica A: Transport Science, 2022
Sen Luan, Xi Chen, Yuelong Su, Zhenning Dong, Xiaolei Ma
To model the path TTD considering the dependency of links, Herring et al. (2010) and Ramezani and Geroliminis (2012) proposed a convolution-based Markov model. These authors assumed that each link has one potential state from a time-invariant state transition matrix and that two states of every two adjacent links form a Markov chain. Chen et al. (2017) introduced a copula model to characterize the path TTD as a multivariate joint distribution and each link TTD as a marginal distribution. Their results indicated that the copula-based model outperforms the convolution models for the reliable calculation of travel time in the path level. In fact, copula is a powerful tool for measuring the dependence between the multivariate joint distributions in finance (Joe 1997; Nelsen 1998; Embrechts, Mcneil, and Straumann 1999) and has been increasingly used in transportation in recent years (Bhat and Eluru 2009; Rashidi and Mohammadian 2016; Zou and Zhang 2016; Ma et al., 2017a; Das and Maurya 2018). However, the multivariate copula function brings complex multivariate probability integral calculations, which are time-consuming and difficult to implement on a large-scale network. Thus, we introduce the copula-based method to simplify this complex calculation.
Predicting adhesive sealing life of Li-ion pouch cell using a fusion method considering time-varying dependence
Published in The Journal of Adhesion, 2021
Kunsong Lin, Liyuan Kou, Yunxia Chen, Biao Zhang
Data-driven methods can efficiently derive reliable results only if historical data are abundant. It has been used in the remaining useful life (RUL) prediction of a single cell.[12–14] As for the dependence modelling, the common approaches include time scale method, bivariate method, conditional correlation method and copula method.[15] The time scale method is supposed to construct on specific relationship assumption (e.g. linear relationship), which is not necessarily accurate. The bivariate method has limitations on the marginal distributions.[16] Compared to others, the copulas have the advantages of flexibility and accuracy, and can be used to model nonlinear, asymmetric, and time-varying dependencies in risk management, derivative asset pricing, option valuation and so on.[17–20]