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We propose a new statistical instrument-free method to tackle the endogeneity problem. The proposed method models the joint distribution of the endogenous regressor and the error term in the structural equation of interest (the structural error) using a copula method, and it makes inferences on the model parameters by maximizing the likelihood derived from the joint distribution. Similar to the \"exclusion restriction\" in instrumental variable methods, extant instrument-free methods require the assumption that the unobserved instruments are exogenous, a requirement that is difficult to meet. The proposed method does not require such an assumption. Other benefits of the proposed method are that it allows the modeling of discrete endogenous regressors and offers a new solution to the slope endogeneity problem. In addition to linear models, the method is applicable to the popular random coefficient logit model with either aggregate-level or individual-level data. We demonstrate the performance of the proposed method via a series of simulation studies and an empirical example.

Such complex causative factors in current failure probability models are represented by simply random uncertainty and completely independent or correlation of failure modes, which can often limit the model utility. In this study, we developed a methodology to construct failure probability models for high fill levees, incorporating the identification of uncertainties and an analysis of failure modes. Based on quantification of stochastic-grey-fuzzy uncertainties, probability analysis involved with overtopping, instability and seepage failure modes was implemented combined with probability and non-probability methods. Given that the interaction among failure modes typically exhibits nonlinear behavior, rather than linear correlation or complete independence, a simple methodology for the binary Copula function was established and implemented in MATLAB. This methodology was applied to the high fill segments of a long-distance water transfer project characterized by high population density. It shows that the failure probability of a single failure mode is overestimated when uncertainties are not considered, because of the randomness and fuzziness of some parameters and the greyness of information. Meanwhile, it is found that the magnitude of failure probability related to levee breach is overestimated without respect to failure modes correlation, especially when the probabilities of seepage and instability are both significant and closely aligned.

Climate change can modify regional wind power generation ability, as it may affect wind speed. Here, we developed a multivariate copula downscaling (MvCD) approach to statistically downscale the near-surface wind speed of CMIP5 global climate models (GCMs) to the scale of wind farms in Urumqi, China. The low computational cost and high random analysis capability of this approach allowed the rapid assessment of projected changes and randomness from nine GCMs, spanning a range of potential futures under four scenarios. Simulation data from multiple GCMs and historical data of the study area were incorporated into the MvCD to generate a high dimensional multivariate copula. Thereafter, the high dimensional multivariate copula was further used to identify future wind speed patterns based on multiple GCMs under different CO2 emission scenarios. The estimated amount of wind power generation was obtained using future wind speed data. Results revealed the regional characteristics and periodicity of wind speed for Urumqi in the future. Wind power generation results revealed the impacts of climate changes on regional wind power generation and indicated that high wind speeds would occur from June to September and low wind speeds would occur from December to March in future scenarios. Wind speed would be more extreme under each scenario in the future than before. The highest and lowest wind speeds will increase and decrease, respectively. Sustained high winds would increase the potential of wind power generation in the future. Wind instability based on CO2 emission increases will lead to wind power being curtailed and low wind-power generation.

The critical role of marketing in driving nonprofit performance has been recognized for decades. However, in practice, there has been a disturbingly weak acknowledgment and/or implementation of marketing practices across nonprofits to date. Marketing is often perceived as an avoidable and costly overhead. The issue is complicated by the fact that nonprofit performance is relatively difficult to measure and may often comprise multiple tangible and intangible outcomes with different (linear and nonlinear) functional forms. Furthermore, nonprofit performance outcomes often depend on behavioral and attitudinal changes of the target segment. The authors address these challenges by presenting a methodology to link marketing efforts to nonprofits’ mission-based performance outcome(s). The authors apply their approach with data from a large nonprofit and find empirical support for the notion that marketing can play a pivotal and significant role in improving nonprofits’ mission-based performance outcomes. The findings help present a strong case for nonprofit leaders and policy makers to fund and treat marketing as a critical investment to drive nonprofit entities’ performance.

To more effectively account for the correlation between components in the seismic reliability analysis of reinforced concrete arch bridges, this study proposes a system seismic reliability analysis method based on the D-vine Copula function. First, based on the theories of seismic vulnerability and hazard, the seismic vulnerability curves of key components (arch ring, piers, main girder, columns) and the site hazard curves are obtained. Second, a trial algorithm is used to determine alternative combinations of Pair-Copula functions. The maximum likelihood estimation method is employed to solve for the parameter θ, and the optimal Pair-Copula function is selected based on AIC and BIC information criteria. The optimal Pair-Copula function for each layer in the D-vine structure is determined through hierarchical iteration, ultimately constructing a seismic reliability evaluation framework for arch bridge systems that incorporates component correlations. The results show that the damage probability of the arch ring is consistently the highest, followed by the piers and main girder, with the columns having the lowest probability. Compared to ignoring component correlation, the seismic reliability indices of the system under minor, moderate, severe damage, and complete failure states all decrease when correlation is considered, indicating that component correlation significantly affects system reliability. Ignoring correlation leads to an overestimation of the system’s seismic performance. The seismic reliability indices obtained by the D-vine Copula method and Monte Carlo simulation are in good agreement, with a maximum relative error not exceeding 2.26%, verifying the applicability and accuracy of the D-vine Copula method in the reliability analysis of complex structural systems. By constructing an accurate joint probability distribution model, this study effectively accounts for the nonlinear correlation characteristics between components. Compared to the traditional Monte Carlo simulation, which relies on large-scale repeated sampling, the D-vine Copula method significantly reduces computational complexity through analytical derivation, improving computational efficiency by over 80%.

Most reliability studies assume large samples or independence among components, but these assumptions often fail in practice, leading to imprecise inference. We address this issue by constructing confidence intervals (CIs) for the reliability of two-component systems with Weibull distributed failure times under a copula-frailty framework. Our construction integrates gamma-distributed frailties to capture unobserved heterogeneity and a copula-based dependence structure for correlated failures. The main contribution of this work is to derive adjusted CIs that explicitly incorporate the copula parameter in the variance-covariance matrix, achieving near-nominal coverage probabilities even in small samples or highly dependent settings. Through simulation studies, we show that, although traditional methods may suffice with moderate dependence and large samples, the proposed CIs offer notable benefits when dependence is strong or data are sparse. We further illustrate our construction with a synthetic example illustrating how penalized estimation can mitigate the issue of a degenerate Hessian matrix under high dependence and limited observations, so enabling uncertainty quantification despite deviations from nominal assumptions. Overall, our results fill a gap in reliability modeling for systems prone to correlated failures, and contribute to more robust inference in engineering, industrial, and biomedical applications.

The interplay of multi-reservoirs is critical in reservoir joint disposal and water conservancy projects. As the flood risk of upstream hydrological stations could be transferred and unevenly distributed to downstream tributary stations, flood risk transfer through multi-reservoirs warrants further investigation. This study proposed a copula simulation approach to develop a joint flood risk distribution of multi-reservoirs (spanning Xianyang, Huaxian County, and Zhangjiashan) in a drainage tributary of the Weihe River. Pair-copulas of each reservoir pair were constructed to analyse the correlations between the reservoir sites. The approach was then used to create a joint flood risk distribution for the reservoirs. The flood risk and corresponding flood volume of Zhangjiashan were calculated based on the flood risk levels of Xianyang and Huaxian County. The results indicate that the flood risks of Huaxian County would be transferred to Xianyang and Zhangjiashan to some extent, and Xianyang could mitigate more flood risks from Huaxian County than from Zhangjiashan. The findings have significance for informed decision-making regarding the Zhangjiashan reservoir construction project.

This article introduces the approach of using Bayesian sampling to estimate the mixture copula with discrete margins, we further apply our models to solve the class imbalanced problems in data science by oversampling. The methodology makes it possible to learn and sample from the data set with the discrete and continuous features exists simultaneously. On the other hand, the discreetness of factors in a data set are not naturally considered for the classic SMOTE algorithm and classic random oversampling is simply performed by generating the already existing points, which do not give any new information to the classifiers and is easy to overfit. Copula methods enable us to generate new points with the correlation structure memorized by learning from the training set. Hence, the overfitting problems are reduced. Experiments with synthetic and real data are done in the article following the introduction of the methodology. The outcomes shows the validity of the approach when compared with the benchmark methods.

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 method for hydrological risk analysis through deriving the bivariate return periods, risk, reliability and bivariate design events; and second, to reveal the impact of marginal distribution selection uncertainty and sampling uncertainty on bivariate design event identification. Particularly, the uncertainties involved in the second goal have not yet received significant consideration. The designed framework for hydrological risk analysis related to flood and extreme precipitation events is exemplarily applied in two catchments of the Loess plateau, China. Results show that (1) distribution derived by the maximum entropy principle outperforms the conventional distributions for the probabilistic modeling of flood and extreme precipitation events; (2) the bivariate return periods, risk, reliability and bivariate design events are able to be derived using the coupled entropy-copula method; (3) uncertainty analysis highlights the fact that appropriate performance of marginal distribution is closely related to bivariate design event identification. Most importantly, sampling uncertainty causes the confidence regions of bivariate design events with return periods of 30 years to be very large, overlapping with the values of flood and extreme precipitation, which have return periods of 10 and 50 years, respectively. The large confidence regions of bivariate design events greatly challenge its application in practical engineering design.

With the increasing penetration of wind power, not only the uncertainties but also the correlation among the wind farms should be considered in the power system analysis. In this paper, Clayton-Copula method is developed to model the multiple correlated wind distribution and a new point estimation method (PEM) is proposed to discretize the multi-correlated wind distribution. Furthermore, combining the proposed modeling and discretizing method with Hybrid Multi-Objective Particle Swarm Optimization (HMOPSO), a comprehensive algorithm is explored to minimize the power system cost and the emissions by searching the best placements and sizes of energy storage system (ESS) considering wind power uncertainties in multi-correlated wind farms. In addition, the variations of load are also taken into account. The IEEE 57-bus system is adopted to perform case studies using the proposed approach. The results clearly demonstrate the effectiveness of the proposed algorithm in determining the optimal storage allocations considering multi-correlated wind farms.