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After a transmission line is covered by ice in winter, ice-shedding and vibration occurs under special meteorological and external dynamic conditions, which leads to intense transmission line shaking. Transmission line ice-shedding and vibration often cause line flashover trips and outages. In January 2018, three 500 kV transmission lines, namely, the 500 kV Guanli line, the 500 kV Dushan line, and the 500 kV Guanqiao line, tripped and cut off due to ice-shedding and vibration in Anhui province, seriously threatening the safe operation of a large power grid. Current studies mainly focus on analyzing the influence factors and characteristics of line ice-shedding and investigating suppression measures, but they only analyze the correlation between each influencing factor and icing or shedding, and do not consider the coupling effects between multiple factors. In this paper, the key influencing factors and the probability distribution of transmission line ice-shedding were analyzed, and a multiple-factor coupling fault probability calculation model of line ice-shedding based on Copula function was proposed. The fault probability was calculated directly by considering multiple influence factors at the same time, which effectively overcame the error caused by multi-factor transformation in fuzzy membership degree and other methods. It provided an important decision-making basis for preventing and controlling transmission line ice-shedding faults. [ABSTRACT FROM AUTHOR]

Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. By using the distribution function or copula of the input variables that comply with such constraints, we derive two types of partial derivatives of functions with non-independent variables (i.e., actual and dependent derivatives) and argue in favor of the latter. Dependent partial derivatives of functions with non-independent variables rely on the dependent Jacobian matrix of non-independent variables, which is also used to define a tensor metric. The differential geometric framework allows us to derive the gradient, Hessian, and Taylor-type expansions of functions with non-independent variables. [ABSTRACT FROM AUTHOR]

In this article, we introduce a novel bivariate probability distribution that is absolutely continuous. Considering the Farlie–Gumbel–Morgenstern (FGM) copula and the unit-Weibull distribution, we can obtain a bivariate unit-Weibull distribution. We evaluate the main properties of the new proposal and use two estimation methods to estimate the parameter for the bivariate probability distribution. A brief Monte Carlo simulation study is conducted to assess the behavior of the employed estimation method and the characteristics of the estimators. Ultimately, as an illustration, a real-life application is presented, demonstrating the utility of the proposal. [ABSTRACT FROM AUTHOR]

With the gradual depletion of surface resources, rock instability caused by deep high stress and mining disturbance seriously affects safe mining. To create effective risk management, a rock instability risk field model using microseismic monitoring data is proposed in this study. Rock instability risk was presented visually in 3D visualization. The in-situ microseismic monitoring data was collected and analyzed to make calculation of peak ground velocity (PGV), peak ground acceleration (PGA), energy flux, energy and seismic moment. Indicator weights of PGV, PGA, energy flux are confirmed by using the analytic hierarchy process (AHP) to calculate risk severity. The Copula function is then used to solve the joint probability distribution function of energy and seismic moment. Then the spatial distribution characteristics of risk can be obtained by data fitting. Subsequently, the three-dimensional (3D) risk field model was established. Meanwhile, the established risk field is verified by comparing monitoring data without disturbance and the blasting data with disturbance. It is suggested that the proposed risk field method could evaluate the regional risk of rock instability reasonably and accurately, which lays a theoretical foundation for the risk prediction and management of rock instability in deep mining. [ABSTRACT FROM AUTHOR]

The instability of seabed slope sediments is the main factor influencing the safety of marine resource development. Therefore, to ensure the safe operation of submarine pipelines under complex and uncertain seabed rock and soil conditions, a reliability model was developed to elucidate the trend of impact-related pipeline damage due to submarine slides. Then, a risk assessment of the damage process of submarine slides impacting pipelines was conducted, which is of great significance for the in-depth safety assessment of pipelines impacted by submarine slides. Based on the copula function, a joint probability distribution model considering the correlation among risk variables was established for rational correlation characterization. A probability analysis method of impact-related pipeline damage attributed to submarine slides based on the copula function was proposed. The Monte Carlo simulation (MCS) method was employed to simulate the random uncertainty in limited observation values and accurately determine the reliability of safe pipeline operation under the action of submarine slides. The conclusions were as follows: (1) Based on the copula function, a joint probability distribution model of risk variables with any marginal distribution function and related structure could be developed. (2) The copula function could reasonably characterize relevant nonnormal distribution characteristics of risk variables and could simulate samples conforming to the distribution pattern of the risk variables. (3) The failure probability calculated with the traditional independent normal distribution model was very low, which could result in a notable overestimation of the reliability of submarine pipelines. [ABSTRACT FROM AUTHOR]

In this paper, we consider a sequential monitoring procedure for detecting changes in copula function. We propose a cusum type of monitoring test based on the empirical copula function and apply it to the detection of the distributional changes in copula function. We investigate the asymptotic properties of the stopping time and show that under regularity conditions, its limiting null distribution is the same as the sup of Kiefer process. Moreover, we utilize the bootstrap method in order to obtain the limiting distribution. A simulation study and a real data analysis are conducted to evaluate our test. [ABSTRACT FROM AUTHOR]

A maximum entropy copula is the copula associated with the joint distribution, with prescribed marginal distributions on [0, 1], which maximizes the Tsallis-Havrda-Chavát entropy with q = 2. We find necessary and sufficient conditions for each maximum entropy copula to be a copula in the class introduced in Rodríguez-Lallena and Úbeda-Flores (2004), and we also show that each copula in that class is a maximum entropy copula. [ABSTRACT FROM AUTHOR]

Pairs trading under the copula approach is revisited in this paper. It is well known that financial returns arising from indices in markets may not follow the features of normal distribution and may exhibit asymmetry or fatter tails, in particular. Due to this, the Laplace distribution is employed in this work to fit the marginal distribution function, which will then be employed in a copula function. In fact, a multivariate copula function is constructed on two indices (based on the Laplace marginal distribution), enabling us to obtain the associated probabilities required for the process of pairs trade and creating an efficient tool for trading. [ABSTRACT FROM AUTHOR]

Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted "copula" models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, "CommonMean.Copula", to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model. [ABSTRACT FROM AUTHOR]

Because rockfill strength and seismic ground motion are dominant factors affecting the slope stability of rockfill dams, it is very important to accurately characterize the distribution of rockfill strength parameters, develop a stochastic ground motion model suitable for rockfill dam engineering, and effectively couple strength parameters and seismic ground motion to precisely evaluate the dynamic reliability of the three-dimensional (3D) slope stability of rockfill dams. In this study, a joint probability distribution model for rockfill strength based on the copula function and a stochastic ground motion model based on the improved Clough-Penzien spectral model were built; the strength parameters and the seismic ground motion were coupled using the GF-discrepancy method, a method for the analysis of dynamic reliability of the 3D slope stability of rockfill dams was proposed based on the generalized probability density evolution method (GPDEM), and the effectiveness of the proposed method was verified. Moreover, the effect of different joint distribution models on the dynamic reliability of the slope stability of rockfill dams was revealed, the effect of the copula function type on the dynamic reliability of the slope stability was analysed, and the differences in the dynamic reliability of the slope stability under parameter randomness, seismic ground motion randomness, and coupling randomness of parameters and seismic ground motion were systematically determined. The results were as follows: the traditional joint distribution models ignored related nonnormal distribution characteristics of rockfill strength parameters, which led to excessively low calculated failure probabilities and overestimations of the reliability of the slope stability; in practice, we found that the optimal copula function should be selected to build the joint probability distribution model, and seismic ground motion randomness must be addressed in addition to parameter randomness. [ABSTRACT FROM AUTHOR]

Mastering the lodging risk of planting environment is of great significance to the optimal layout of maize varieties and the breeding of lodging resistant varieties. However, the existing lodging risk models are still at the stage of single or multi-factors independent analysis, and lack of assessment for different lodging types. To address this issue, based on the mechanism of different lodging types, the Archimedean copula function was used to describe the joint probability distribution of wind speed and precipitation, and the lodging risk assessment model of maize was established. By comparing the goodness of fit, when the rank correlation coefficient of these two is positive and negative, the corresponding optimal joint probability distribution functions are the Gumbel copula and Frank copula. According to the spatial distribution of lodging risk, the area from Liaodong Bay northward to Tongyu, Jilin province in the Northeast and the North China Plain has a high frequency of lodging, in which the probability of stalk lodging is two to four times that of root lodging. Finally, we discussed how to apply the lodging risk distribution results to optimize the maize variety test sites to improve the efficiency and reliability of the existing test system. The method proposed in this paper comprehensively considers the synergistic effect of multiple factors and can provide technical support for other risk assessment. [ABSTRACT FROM AUTHOR]

All but one of the copulas in a recent paper in Symmetry by Perlman and Wellner can be identified as particular members of either the beta or t families of elliptical copulas. [ABSTRACT FROM AUTHOR]

Do there exist circular and spherical copulas in ℝd? That is, do there exist circularly symmetric distributions on the unit disk in ℝ² and spherically symmetric distributions on the unit ball in ℝd, d ≥ 3, whose one-dimensional marginal distributions are uniform? The answer is yes for d = 2 and 3, where the circular and spherical copulas are unique and can be determined explicitly, but no for d ≥ 4. A one-parameter family of elliptical bivariate copulas is obtained from the unique circular copula in ℝ² by oblique coordinate transformations. Copulas obtained by a non-linear transformation of a uniform distribution on the unit ball in ℝd are also described, and determined explicitly for d = 2. [ABSTRACT FROM AUTHOR]

A Bayesian hierarchical framework with a Gaussian copula and a generalized extreme value (GEV) marginal distribution is proposed for the description of spatial dependencies in data. This spatial copula model was applied to extreme summer temperatures over the Extremadura Region, in the southwest of Spain, during the period 1980–2015, and compared with the spatial noncopula model. The Bayesian hierarchical model was implemented with a Monte Carlo Markov Chain (MCMC) method that allows the distribution of the model's parameters to be estimated. The results show the GEV distribution's shape parameter to take constant negative values, the location parameter to be altitude dependent, and the scale parameter values to be concentrated around the same value throughout the region. Further, the spatial copula model chosen presents lower deviance information criterion (DIC) values when spatial distributions are assumed for the GEV distribution's location and scale parameters than when the scale parameter is taken to be constant over the region. [ABSTRACT FROM AUTHOR]

Symmetric elliptical distributions have been intensively used in data modeling and robustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector μ is the location parameter, Σ : p × p is the positive definite scale parameter, p-vector α is the skewness or shape parameter, and the number of degrees of freedom ν is fixed. Special attention is paid to the two-parameter distribution when μ = 0 that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of Σ and α. Convergence to the asymptotic distributions is examined in simulation experiments. [ABSTRACT FROM AUTHOR]

A copula is a multivariate cumulative distribution function with marginal distributions U n i f o r m (0 , 1) . For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis. [ABSTRACT FROM AUTHOR]

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student's t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student's t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples. [ABSTRACT FROM AUTHOR]

Inventory-pooling (IP) is an effective tool to mitigate demand uncertainty and variability, to reduce operational costs, and consequently to increase the profit. The major assumptions of the previous works in literature on IP include the following: (1) Independents demand, which satisfy the typical normal independent and identically distributed (iid) random variables; (2) dependents (correlated) symmetric demands, which follows to a multivariate normal distribution. The effect of the dependent asymmetric demand is not yet studied. The aim of this paper is to consider this more realistic case. Indeed, the contribution of this paper is twofold. Firstly, it analyzes both the sensitivity of dependence structure and the levels of skewness of distributions on IP policies in terms of optimal total cost and demand satisfaction constraint. Secondly, both symmetric and asymmetric demand distributions are modeled using various beta distribution and the dependance between demands are modeled using various copulas. A newsvendor problem inspired by the literature, with two decentralized locations and two centralized locations, is considered the empirical study. For each dependance situation, three IP models are considered: inventory centralization, regular transshipments, and independent systems. The results suggest divergences in the decisions in about 9% of cases. Bad choice of marginal distributions given that the copula is appropriate can lead to divergences that vary between 2.2% and 4%, depending on whether the demand distributions are symmetric or asymmetric. [ABSTRACT FROM AUTHOR]

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators. It is shown that most of the well-known Archimedean copulas can be generated using such distributions. Further, we introduced new Archimedean copulas. [ABSTRACT FROM AUTHOR]

Pareto type II distribution has been studied from many statisticians due to its important role in reliability modelling and lifetime testing. In this article, we introduce two bivariate Pareto Type II distributions; one is derived from copula and the other is based on mixture and copula. Parameter Estimates of the proposed distribution are obtained using the maximum likelihood method. The performance of the proposed bivariate distributions is examined using a simulation study. Finally, we analyze one data set under the proposed distributions to illustrate their flexibility for real-life applications. [ABSTRACT FROM AUTHOR]

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period. [ABSTRACT FROM AUTHOR]