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The assumption of conditional symmetry, which implies that the distribution of one random variable given another random variable has a symmetric form, plays a crucial role in various probability and statistics problems. This study aims to examine copula properties related to the conditional symmetry/asymmetry of two random variables. We investigate the possibility of ordering copulas based on their level of conditional asymmetry, similar to the concordance ordering for dependence. To quantify the degree of conditional asymmetry of a copula, we introduce measures that are monotonic for the proposed ordering. The characteristics of the proposed order and measures are elaborated upon. Several examples are included to demonstrate the results. [ABSTRACT FROM AUTHOR]

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies. [ABSTRACT FROM AUTHOR]

In this study, we propose the application of the GARCH‐EVT‐Copula model in estimating liquidity‐adjusted value‐at‐risk (L‐VaR) of energy stocks while modeling nonlinear dependence between return and bid‐ask spread. Using the L‐VaR framework of Bangia et al. (1998), we present a more parsimonious model that effectively captures non‐zero skewness, excess kurtosis, and volatility clustering of both return and spread distributions of energy stocks. Moreover, to measure the nonlinear dependence between return and spread series, we use multiple copulas: Clayton, Gumbel, Frank, Normal, and Student‐t. Based on the statistical backtesting and economic loss functions, our results suggest that the GARCH‐EVT‐Clayton copula is superior and most consistent in forecasting L‐VaR compared with other competing models. This finding has several implications for investors, market makers, and daily traders who appreciate the importance of liquidity in market risk computation. [ABSTRACT FROM AUTHOR]

The Sharpe ratio is a widely used tool for assessing investment strategy performance. An essential part of investing involves creating an appropriate portfolio by determining the optimal weights for desired assets. Before constructing a portfolio, selecting a set of investment opportunities is crucial. In the absence of a risk-free asset, investment opportunities can be identified based on the Sharpe ratios of risky assets and their correlation. The maximum squared Sharpe ratio serves as a useful metric that summarizes the performance of an investment opportunity in a single value, considering the Sharpe ratios of assets and their correlation coefficients. However, the assumption of a normal distribution in asset returns, as implied by the Sharpe ratio and related metrics, may not always hold in practice. Non-normal returns with a non-linear dependence structure can result in an overestimation or underestimation of these metrics. Copula functions are commonly utilized to address non-normal dependence structures. This study examines the impact of asset dependence on the squared maximum Sharpe ratio using copulas and proposes a copula-based approach to tackle the estimation issue. The performance of the proposed estimator is illustrated through simulation and real-data analysis. [ABSTRACT FROM AUTHOR]

To precisely represent bivariate continuous variables, this work presents an innovative approach that emphasizes the interdependencies between the variables. The technique is based on the Teissier model and the Farlie-Gumbel-Morgenstern (FGM) copula and seeks to create a complete framework that captures every aspect of associated occurrences. The work addresses data variability by utilizing the oscillatory properties of the FGM copula and the flexibility of the Teissier model. Both theoretical formulation and empirical realization are included in the evolution, which explains the joint cumulative distribution function F (z 1 , z 2) , the marginals F (z 1) and F (z 2) , and the probability density function (PDF) f (z 1 , z 2) . The novel modeling of bivariate lifetime phenomena that combines the adaptive properties of the Teissier model with the oscillatory characteristics of the FGM copula represents the contribution. The study emphasizes the effectiveness of the strategy in controlling interdependencies while advancing academic knowledge and practical application in bivariate modelling. In parameter estimation, maximum likelihood and Bayesian paradigms are employed through the use of the Markov Chain Monte Carlo (MCMC). Theorized models are examined closely using rigorous model comparison techniques. The relevance of modern model paradigms is demonstrated by empirical findings from the Burr dataset. [ABSTRACT FROM AUTHOR]

There has been much work on the distribution of independent or dependent random variables. But we are not aware of any work giving exact results for the distribution of the sum of randomly weighted random variables. In this paper, we derive exact results for the randomly weighted sum of two dependent random variables. The derived expressions are for the cumulative distribution function, conditional expectation, moment generating function, value at risk, expected shortfall and the limiting tail behavior of the randomly weighted sum of two dependent random variables. Two numerical illustrations are given. [ABSTRACT FROM AUTHOR]

The Sharpe ratio is a widely used tool for assessing investment strategy performance. An essential part of investing involves creating an appropriate portfolio by determining the optimal weights for desired assets. Before constructing a portfolio, selecting a set of investment opportunities is crucial. In the absence of a risk-free asset, investment opportunities can be identified based on the Sharpe ratios of risky assets and their correlation. The maximum squared Sharpe ratio serves as a useful metric that summarizes the performance of an investment opportunity in a single value, considering the Sharpe ratios of assets and their correlation coefficients. However, the assumption of a normal distribution in asset returns, as implied by the Sharpe ratio and related metrics, may not always hold in practice. Non-normal returns with a non-linear dependence structure can result in an overestimation or underestimation of these metrics. Copula functions are commonly utilized to address non-normal dependence structures. This study examines the impact of asset dependence on the squared maximum Sharpe ratio using copulas and proposes a copula-based approach to tackle the estimation issue. The performance of the proposed estimator is illustrated through simulation and real-data analysis.

In this paper, we examine various characteristics of both base and peak electricity spot prices and their returns, and investigate dependence structures, extreme co-movements, risk spillovers, and integration relationships among the five major European electricity markets, including France, Germany, the Netherlands, Spain, and the UK. To do so, we propose a new perspective by applying a hybrid of ARMA-GARCH, static and dynamic copulas, and dynamic state-space models with the Kalman filter to address the issue. Based on the results of the ARMA-GJR-GARCH model, we first find that there are spillover effects in the returns of both base and peak spot prices in the five European electricity markets, and there are heteroskedastic, asymmetric, and leverage effects with negative and positive shocks, including spikes and drops during both base and peak load periods. Hence, a decrease in prices will boom the variance of the returns, and a decrease in returns can lead to a much greater increase in volatility. Second, there exist some extents of positive dependencies, tail dependencies, and extreme co-movements among the European electricity markets based on the copula models. In addition, we find that the degree of (tail) dependence and the potential state of market integration are stronger and higher during the peak period than the base period, implying that the European electricity markets could boom or crash together, especially during the peak load period. Further, the results of both the dynamic copulas and dynamic state-space models show that most pairs of the European electricity markets co-move symmetrically and have a time-varying dependence, but do not appear to grow over time. Finally, we provide an application of the copula-GARCH model in estimating and predicting risk spillovers across the five European electricity markets. We document that there are high-risk spillover effects in the European electricity markets because the values of the Conditional Value-at-Risk (CoVaR) are large. Also, we find that the more integrated the market, the more the systematic risk contribution of the market as indicated by ΔCoVaR. Our findings provide useful information regarding the dependence, integration, risk management, and asset pricing for the European electricity markets.

Flooding in low-lying coastal zones arises from coastal (storm surge, tides, and waves), fluvial (excessive river discharge), and pluvial (excessive surface runoff) drivers. We analyse changes in compound flooding potential around the contiguous United States (CONUS) coastline stemming from select combinations of these flooding drivers using long observational records with at least 55 years of data. We assess temporal changes in the tail (extremal) dependence (χ) using a 30-year sliding time window. Periods of strong tail dependence are found for the windows centered between the 1960s and 1980s/1990s at several locations for surge-discharge (S-Q) and surge-precipitation (S–P) combinations. Changes in dependence are associated with large-scale climate indices such as the Arctic Oscillation (AO) and El Nino Southern Oscillation indices (Niño 1.2 and Niño 3), among others. The significance of potential changes in the dependence structure is subsequently tested using Kullback–Leibler (KL) divergence. We find that changes are mostly not significant. Finally, we perform a complete multivariate statistical analysis exemplarily for one selected pair of variables at one location (S-Q in Washington, DC), allowing for varying dependence strength and structure as well as changes in the marginal distributions. Combined changes with increase in the dependence and marginals exacerbate the predicted compound flood potential. The comprehensive analysis presented here provides new insights into how and where compound flooding potential has changed with time, demonstrates associated links with large-scale climate indices, and highlights the effects of changes in the dependence and marginals in a multivariate statistical framework.

Recent advances in medical instruments, information technology, and unprecedented data sharing allowed scientists to investigate, trace, and monitor the COVID-19 pandemic faster than any previous outbreak. This extraordinary speed makes COVID-19 a medical revolution that causes some unprecedented analyses, discussions, and models. Modeling the dependence between the number of tests and the positivity rate is one of these new issues. Using four classes of copulas (Clayton, Frank, Gumbel, and FGM), this study is the first attempt tom model the dependency. The estimation of the parameters of the copulas is obtained using the maximum likelihood method. To evaluate the goodness of fit of the copulas, we calculate AIC. The computations are conducted on Matlab R2015b, R 4.0.3, Maple 2018a, and EasyFit 5.6. Findings indicate that at the beginning of a typical epidemic, the number of tests is relatively low and the proportion of positivity is high. As time passes, the number of tests increases, and the positivity rate decreases. The epidemic peaks are occasions that violate the stated general rule –due to the early growth of the number of tests. Also, during both peak and non-peak times, the rising number of tests is accompanied by decreasing the positivity rate. We find that the proportion of positivity is more proportional than the number of tests to the number of infected cases. Therefore, the changes in the positivity rate can be considered a representative of the level of the spreading. Approaching zero positivity rate is a good criterion to scale the success of a healthcare system in fighting against an epidemic. Accordingly, the number and accuracy of tests can play a vital role in the quality level of epidemic data. [ABSTRACT FROM AUTHOR]

We determine the upper and lower bounds for possible values of Kendall's tau of a bivariate copula given that the value of its Spearman's footrule or Gini's gamma is known, and show that these bounds are always attained. [ABSTRACT FROM AUTHOR]

Motivated by (random) lifetimes of electronic components or financial institutions we study the problem of maximizing the probability that (i) a random variable X is not smaller than another random object Y and (ii) that X and Y coincide within the class of all random variables X , Y with given univariate continuous distribution functions F and G , respectively. We show that the maximization problems correspond to finding copulas maximizing the mass of the endograph Γ ≤ (T) = { (x , y) ∈ [ 0 , 1 ] 2 : y ≤ T (x) } and the graph Γ (T) = { (x , T (x)) : x ∈ [ 0 , 1 ] } of T = G ∘ F − , respectively. After providing simple, copula-based proofs for the existence of copulas attaining the two maxima m ¯ T and w ¯ T we generalize the obtained results to the case of general (not necessarily monotonic) transformations T : [ 0 , 1 ] → [ 0 , 1 ] and derive simple and easily calculable formulas for m ¯ T and w ¯ T involving the distribution function F T of T (interpreted as random variable on [ 0 , 1 ]). The latter are then used to characterize all non-decreasing transformations T : [ 0 , 1 ] → [ 0 , 1 ] for which m ¯ T and w ¯ T coincide. A strongly consistent estimator for m ¯ T is derived and proven to be asymptotically normal under very mild regularity conditions. Several examples and graphics illustrate the main results and falsify some seemingly natural conjectures, an application of some of the obtained results to the seemingly unrelated topic of relative effects indicates the importance of the tackled questions. • Simple formulas for maximum/minimum prior/joint default probability are derived. • The situation of the two probabilities coinciding is characterized. • A strongly consistent estimator for the prior default probability is established. • The estimator is shown to be asymptotically normal. • An application to relative effects is given. [ABSTRACT FROM AUTHOR]

Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and investigate theoretically new two-dimensional copulas based on trigonometric functions modulated by a tuning angle parameter. The independence copula is, thus, extended in an original manner. Conceptually, the proposed trigonometric copulas are ideal for modeling correlations into periodic, circular, or seasonal phenomena. We examine their qualities, such as various symmetry properties, quadrant dependence properties, possible Archimedean nature, copula ordering, tail dependences, diverse correlations (medial, Spearman, and Kendall), and two-dimensional distribution generation. The proposed copulas are fleshed out in terms of data generation and inference. The theoretical findings are supplemented by some graphical and numerical work. The main results are proved using two-dimensional inequality techniques that can be used for other copula purposes.

In this paper, we consider series systems consisting of arbitrary dependent components. We study the residual lifetimes of such systems based on copulas family from a new point of view. First, we extract a new explicit expression for the reliability functions of residual lifetimes of the systems. Moreover, we give some stochastic ordering properties for the residual lifetimes of series systems based on the dependence structure of the components and the corresponding mean functions. The results are expanded for series systems having used components of age t > 0. Subsequently, the problem of the stochastic comparison of a series system having used components and a used series system has been considered. To show the application of results, we provide some numerical examples. Finally, we present some dependence properties of the residual lifetimes of series system based on the properties of the lifetimes of components. [ABSTRACT FROM AUTHOR]

This paper examines correlation and dependence structures between money and the level of economic activity in the USA in the context of a Markov-switching copula vector error correction model. We use the error correction model to focus on the short-run dynamics between money and output while accounting for their long-run equilibrium relationship. We use the Markov regime-switching model to account for instabilities in the relationship between money and output, and also consider different copula models with different dependence structures to investigate (upper and lower) tail dependence. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite System (GNSS) signals scan the earth’s atmosphere with a high spatiotemporal resolution. They have promoted the application of the GNSS networks as an imaging system for the tomographic reconstruction of wet refractivity N w .To come up with a unique solution of this inverse problem and to preserve the atmospheric dynamics intact by solution, the resolution of reconstructed images of wet refractivityis usually increased. We propose a Copula-based approach as a geometry-free technique to develop a tomography network over southwest Germany and a part of France. Here, we apply the estimated N w time series from Weather Research and Forecasting model from April to October 2016 and evaluate the pixel-wise dependence structure and dissimilarity measures of the N w time series at seven pressure levels from 949.2 to 263.8 hPa. At each level, the most appropriate dissimilarity measure to give an optimal resolution is identified based on the percentage of pair pixels with asymmetric Copulas. Then, the optimum resolution is identified by evaluating the distance-based variations of dissimilarity values. The investigations propose a non-uniform tomography network for this region. Furthermore, we assess the geometry of the problem by investigating the resolution matrix of the tomography model in all hourly time epochs of Day of Year (DoY) 279. According to the results, using uniform voxel size for tomography reconstruction in the area leads to missing information in the lower parts of the troposphere. Moreover, we show that combining our method and resolution matrix provides a mathematical tool for deciding on the required compromise between the geometry and dynamics in Global Positioning System (GPS) tomography. [ABSTRACT FROM AUTHOR]

A new Archimedean copula family is presented that was derived from the SAHARA utility function introduced in the economic literature in 2011. Its properties are discussed, and its flexibility and versatility are demonstrated. It is left tail decreasing or right tail increasing, but unlike mainstream Archimedean families, not necessarily stochastically increasing at the same time. It is shown that the family fits very well to a dataset of previously studied coupled lives in the literature. [ABSTRACT FROM AUTHOR]

In this article, the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones, shown to imply other usual postulates. While other popular choices are proved to violate some of these requirements, a class of dependence measures satisfying all of them is identified. One particular measure, that we call the Hellinger correlation, appears as a natural choice within that class due to both its theoretical and intuitive appeal. A simple and efficient nonparametric estimator for that quantity is proposed, with its implementation publicly available in the R package HellCor. Synthetic and real-data examples illustrate the descriptive ability of the measure, which can also be used as test statistic for exact independence testing. for this article are available online. [ABSTRACT FROM AUTHOR]

The dependence structure of the life statuses plays an important role in the valuation of life insurance products involving multiple lives. Although the mortality of individuals is well studied in the literature, their dependence remains a challenging field. In this paper, the main objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple. It is intended to describe in a dynamic framework the joint mortality of married couples in terms of marginal mortality rates. The proposed framework is general and aims to capture, by adjusting some parametric form, the desired effect such as the "broken-heart syndrome". To this end, we use a well-suited multiplicative decomposition, which will serve as a building block for the framework to relate the dependence structure and the marginals, and we make the link with existing practice of affine mortality models. Finally, given that the framework is general, we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics. [ABSTRACT FROM AUTHOR]

We investigate the volatility dynamics of commodity price and the dependence structure between commodity prices and output growth in the G7 and EM7 economies using a semiparametric GARCH-in-Mean copula approach. We show that for the G7 economies, a symmetric weak tail dependence exists between commodity prices and outputs in France, Germany, and Japan. For the EM7 economies, a lower tail dependence is observed between commodity prices and output growth in Brazil, and a symmetric weak tail dependence is observed in Indonesia. No statistically significant tail dependence between commodity prices and output growth is found for the rest of the G7 and EM7 economies. [ABSTRACT FROM AUTHOR]

A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula‐based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re‐emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula‐based modeling. Here, we (1) provide end‐users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user‐friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion. This article is categorized under:Science of Water > Hydrological ProcessesScience of Water > Methods [ABSTRACT FROM AUTHOR]

Copulas are important probabilistic tools to model and interpret the correlations of measures involved in real or experimental phenomena. The versatility of these phenomena implies the need for diverse copulas. In this article, we describe and investigate theoretically new two-dimensional copulas based on trigonometric functions modulated by a tuning angle parameter. The independence copula is, thus, extended in an original manner. Conceptually, the proposed trigonometric copulas are ideal for modeling correlations into periodic, circular, or seasonal phenomena. We examine their qualities, such as various symmetry properties, quadrant dependence properties, possible Archimedean nature, copula ordering, tail dependences, diverse correlations (medial, Spearman, and Kendall), and two-dimensional distribution generation. The proposed copulas are fleshed out in terms of data generation and inference. The theoretical findings are supplemented by some graphical and numerical work. The main results are proved using two-dimensional inequality techniques that can be used for other copula purposes. [ABSTRACT FROM AUTHOR]

Copula modelling is a popular tool in analysing the dependencies between variables. Copula modelling allows the investigation of tail dependencies, which is of particular interest in risk and survival applications. Copula modelling is also of specific interest to economic and financial modelling as it can help in the prediction of financial contagion and periods of "boom" or "bust". Bivariate copula modelling has a rich variety of copulas that may be chosen to represent the modelled dataset dependencies and possible extreme events that may lie within the dataset tails. Financial copula modelling tends to diverge as this richness of copula types within the literature may not be well realised with the two different types of modelling, one being non-time-series and the other being time-series, being undertaken differently. This paper investigates standard copula modelling and financial copula modelling and shows why the modelling strategies in using time-series and non-time-series copula modelling is undertaken using different methods. This difference, apart from the issues surrounding the time-series component, is mostly due to standard copula modelling having the ability to use empirical CDFs for the probability integral transformation. Financial time-series copula modelling uses pseudo-CDFs due to the standardized time-series residuals being centred around zero. The standardized residuals inhibit the estimation of the possible distributions required for constructing the copula model in the usual manner. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of characterizing all functions f : [ 0 , 1 ] → R + such that C f (x , y) = x y f ((1 − x) (1 − y)) , x , y ∈ [ 0 , 1 ] is a bivariate copula. We provide a complete characterization for the two cases: (i) when C f is, in addition, totally positive of order 2 (TP 2) and (ii) when f is twice continuously differentiable. In general, the function f need only be twice differentiable Lebesgue almost everywhere as shown by investigating necessary conditions for C f to be a copula. The paper also contains numerous examples illustrating obtained results and connections to known facts from the literature. Moreover, several properties of such copulas are described. [ABSTRACT FROM AUTHOR]

This paper re-examines the dependence structure between uncertainty in oil prices and sovereign credit risk of oil exporters. To address this issue, we employ a copula approach that allows us to capture asymmetric and nonlinear dependence structures. Empirical analyses involve daily data of the 5-year sovereign credit default swaps spreads and the crude oil implied volatility from January 2010 to May 2019, covering a sample of ten oil-exporting countries. Except for Brazil and Venezuela, our results provide evidence of significant positive and upper tail dependence in the relationship between oil market uncertainty and oil exporters' sovereign risk. Overall, our findings highlight that high uncertainty in oil prices coincides with large-scale increases in the sovereign credit risk of oil-exporting countries, supporting the hypothesis that investors, exposed to economic losses from risk events in oil exporters, are all the more pessimistic that prevails high uncertainty about future oil prices. Our findings have implications for oil exporter' policymakers as well as investors. • We study the relationship between oil price volatility and the sovereign risk of oil exporters. • We use daily data of the sovereign CDS spreads and the crude oil implied volatility. • We provide evidence of positive and upper tail dependence in the relationship. • High uncertainty in oil prices coincides with a surge in the sovereign CDS spreads of oil exporters. [ABSTRACT FROM AUTHOR]

The two-tier stochastic frontier model has seen widespread application across a range of social science domains. It is particularly useful in examining bilateral exchanges where unobserved side-specific information exists on both sides of the transaction. These buyer and seller specific informational aspects offer opportunities to extract surplus from the other side of the market, in combination also with uneven relative bargaining power. Currently, this model is hindered by the fact that identification and estimation relies on the potentially restrictive assumption that these factors are statistically independent. We present three different models for empirical application that allow for varying degrees of dependence across these latent informational/bargaining factors. [ABSTRACT FROM AUTHOR]

It is important for Indonesia as a country with agricultural bases to develop crop insurance. Until now, Indonesia has not had any insurance for horticultural crops other than for corn. This paper discusses horticultural multicrop insurance products based on revenue risk that can be triggered by low prices, low yields, or a combination of both. In designing multicrop insurance products, it is important to model the variability of revenue risk through the implementation of copula toward crop yield and price and to estimate indemnity of the revenue-based multicrop insurance. The analysis employed Gumbel and Clayton copulas to model the dependency structure between crop yield and price of multicrops. Each marginal variable was modeled by using the ARIMA model. The results showed that multicrop revenue insurance tends to reduce the price of agricultural insurance in Indonesia, and thus this program has the potential to have good acceptance in agricultural insurance. [ABSTRACT FROM AUTHOR]

The theory of the natural hedge states that agricultural yields and prices are inversely related. Actuarial rules for U.S. crop revenue insurance assume that dependence between yield and price is constant across all counties within a state and that dependence can be adequately described by the Gaussian copula. We use nonlinear measures of association and a selection of bivariate copulas to empirically characterize spatially-varying dependence between prices and yields and examine premium rate sensitivity for all corn producing counties in the United States. A simulation analysis across copula types and parameter values exposes hypothetical impacts of actuarial changes.

Based on copula applications, the work points out the use of cumulative distribution function for the characteristics bivariate cases and the connections among them. The analyzed variables, Brinell Hardness and Tensile Strength, are joined in a cumulative distribution function (CDF) to present and forsee the output variable, the copula function. A method using the bivariate density and cumulative distribution function with the Clayton copula, and Gamma distribution is herein analyzed. The dependence between two important mechanical properties is studied and assed.

The copula is well-known for learning scale-free measures of dependence among variables and has invited much interest in recent years. At the very coronary heart of the copula, the concept is the well-known theorem of Sklar. It states that any multivariate distribution function can be disintegrated into the marginal distributions and a copula, which comprises the reliance between variables. On the other hand, the decision tree is a renowned nonparametric dominant modeling approach used for both regression and labeling problems. A decision tree represents a tree-structured classification of the data into surprising instructions for simplicity and prediction reason. In this paper, we are going to appraise with novel nonparametric copula-based decision tree organization using a measure of dependence: maximal information coefficient as classification index for two related variables which best classify the data concerning looking at the factors, but additionally ranked the factors in line with their inferences. Additionally, we pre-test the splitting criteria value to anticipate growing branches of the decision tree at each infant node. For example, we followed our proposed method to credit card records for Taiwan and coronary heart disease records of Pakistan and acquired the desirable outcomes. As a result, the anticipated method of initiating two-variable decision trees is tested using constructive tools for classification, prediction and reconnecting critical factors in statistics, finance, fitness sciences, machine learning, and many other associated fields. [ABSTRACT FROM AUTHOR]

Rainfall and temperature remain the two major climatic parameters influencing agriculture productivity, meteorology and weather related industries. It is known that accurate analysis and simulation of temperature and rainfall processes is difficult due to the interdependence between them. This study provides an alternative approach by modeling rainfall and temperature processes using Frank copula from Archimedean family to derive a bi-variate model and measure the dependence between them. The copula approach is flexible in that it enables independent modeling of marginal behavior and dependence between the variables besides providing information on both the structure and degree of dependence. The study used historical daily rainfall and daily average temperature data for 20 years covering the period from 1995 to 2015 collected by Malawi’s meteorological services for Balaka district. Results of the study indicate that temperature and rainfall are positively correlated based on Kendall tau correlation test. Using the derived bi-variate model we simulated daily average temperature and daily rainfall data which behaved same way as the actual data.

A new Archimedean copula family is presented that was derived from the SAHARA utility function introduced in the economic literature in 2011. Its properties are discussed, and its flexibility and versatility are demonstrated. It is left tail decreasing or right tail increasing, but unlike mainstream Archimedean families, not necessarily stochastically increasing at the same time. It is shown that the family fits very well to a dataset of previously studied coupled lives in the literature.

We describe the R package kdecopula (current version 0.9.2), which provides fast implementations of various kernel estimators for the copula density. Due to a variety of available plotting options it is particularly useful for the exploratory analysis of dependence structures. It can be further used for accurate nonparametric estimation of copula densities and resampling. The implementation features spline interpolation of the estimates to allow for fast evaluation of density estimates and integrals thereof. We utilize this for a fast renormalization scheme that ensures that estimates are bona fide copula densities and additionally improves the estimators' accuracy. The performance of the methods is illustrated by simulations.

We analyze the spatial default dependence between pairs of nonconforming securitized mortgages, originated in Los Angeles between 2000 and 2011 and clustered by zip code. Our approach allows us to estimate the range and shape of the spatial dependence function, which relates zip-code center-to-center distance between mortgages to the dependence parameter of a number of different copulas. We find significant evidence for the presence of spatial dependence, which decays to zero within 40km and can be well characterized by a squared exponential function, a special case of the Matérn spatial correlation function. [ABSTRACT FROM AUTHOR]

Modeling high‐dimension dependence is a challenging problem since it involves too many parameters. In this paper, aquasi‐Monte Carlo (QMC) method based probabilistic load flow computation algorithm, which uses truncated regular vine copula and considers high‐dimension dependence of wind powers, is proposed. Firstly, the regular vine copulas, which use bivariate copulas as building blocks, are used to construct the primary high dimensional dependence. Then, truncation technology is adopted to reduce the computation burden and the memory consumption caused by the rapidly increased parameters number of input variables. Meanwhile, the nonparametric kernel estimation is used to estimate the wind speed marginal distributions and the bandwidth of kernel function is obtained by the direct plug‐in method. Further, QMC method is integrated into the probabilistic power flow computation for obtaining the sampled data of input variables. By the numerical simulation experiments on the modified IEEE 118‐bus power system, the superiority of the proposed probabilistic load flow computation method is verified. [ABSTRACT FROM AUTHOR]

Inspired by the correlation matrix and based on the generalized Spearman's ρ and Kendall's τ between random variables proposed in Lu et al. (J Nonparametr Stat 30(4):860–883, 2018), ρ -matrix and τ -matrix are suggested for multivariate data sets. The matrices are used to construct the ρ -measure and the τ -measure among random vectors with statistical estimation and the asymptotic distributions under the null hypothesis of independence that produce the nonparametric tests of independence for multiple vectors. Simulation results demonstrate that the proposed tests are powerful under different grouping of the investigated random vector. An empirical application to detecting dependence of the closing price of a portfolio of stocks in NASDAQ also illustrates the applicability and effectiveness of our provided tests. Meanwhile, the corresponding measures are applied to characterize strength of interdependence of that portfolio of stocks during the recent two years. [ABSTRACT FROM AUTHOR]

This note studies the dependence of joint mix random vectors from the perspective of covariance matrix. We first provide two useful methods in simulations to construct joint mix for Normal distribution. Then, we propose to characterize joint mix by covariance matrix for general marginal distribution. We present some examples showing that our methodology could provide supplementary results to relevant studies in literature. [ABSTRACT FROM AUTHOR]

Rising sea levels caused by climate change are increasing the risk of overtopping on coastal structures. Moreover, there is a growing societal concern about the visual impact of these structures, which leads to the lowering of their crest freeboards. In previous studies, safety during overtopping events was assessed considering the overtopping layer thickness (h c), the overtopping flow velocity (u c) and the individual wave overtopping volume (V). Existing models in the literature to estimate h c , u c and V on mound breakwater crests are mainly deterministic, involve a chain of successive estimations leading to accumulated errors and/or do not account for the dependencies between h c , u c and V. This study proposes a model to describe the joint probability distribution of h c , u c and V based on bivariate copulas. Experimental data from small-scale 2D physical tests conducted on mound breakwaters with three armor layers (single-layer Cubipod®, and double-layer cubes and rocks) in depth-limited breaking wave conditions on two mild bottom slopes and dimensionless crest freeboards between 0.33 and 3.20 is used. Lognormal distribution functions are proposed for each variable and a multivariate dependence model is developed through a one-tree vine-copula. The parameters of this model are quantified directly using wave characteristics and the structure geometry minimizing the accumulated errors in the final predictions. The application of the model is illustrated by computing the probability of not fulfilling at least a tolerability limit for one of the studied variables (OR probability). The OR probability is computed both considering the dependence and assuming independence between the variables and a significant difference is obtained. It is concluded that by accounting for the multivariate dependence between the variables, it is possible to reduce the crest freeboard and, thus, achieve a more economic design within the required safety level. • Distribution functions are proposed to describe each overtopping variable. • A one-tree vine-copula is proposed to model the dependence of overtopping variables. • The model allows to compute the probability of not fulfilling at least one limit. • The model is quantified based on wave characteristics and structure geometry. [ABSTRACT FROM AUTHOR]

All branches of ecology study relationships among and between environmental and biological variables. However, standard approaches to studying such relationships, based on correlation and regression, provide only some of the complex information contained in the relationships. Other statistical approaches exist that provide a complete description of relationships between variables, based on the concept of the copula; they are applied in finance, neuroscience and elsewhere, but rarely in ecology. We explore the concepts that underpin copulas and the potential for those concepts to improve our understanding of ecology. We find that informative copula structure in dependencies between variables is common across all the environmental, species-trait, phenological, population, community, and ecosystem functioning datasets we considered. Many datasets exhibited asymmetric tail associations, whereby two variables were more strongly related in their left compared to right tails, or vice versa. We describe mechanisms by which observed copula structure and tail associations can arise in ecological data, including a Moran-like effect whereby dependence structures are inherited from environmental variables; and asymmetric or nonlinear influences of environments on ecological variables, such as under Liebig's law of the minimum. We also describe consequences of copula structure for ecological phenomena, including impacts on extinction risk, Taylor's law, and the temporal stability of ecosystem services. By documenting the importance of a complete description of dependence between variables, advancing conceptual frameworks, and demonstrating a powerful approach, we encourage widespread use of copulas in ecology, which we believe can benefit the discipline. [ABSTRACT FROM AUTHOR]

In this paper, we focus our attention on multidimensional copula models for returns of the indexes of selected prominent international financial markets. Our modeling results, based on elliptic copulas, 7-dimensional hierarchical Archimedean copulas, vine copulas and factor copulas demonstrate a dominant role of the SPX index among the considered major stock indexes (mainly at the first tree of the optimal vine copulas). Some interesting weaker conditional dependencies can be detected at it's highest trees. Interestingly, while global optimal model (for the whole period of 277 months) belong to the Factor FDG copulas class, the optimal local models can be found (with very minor differences in the values of GoF test statistic) in the classes of Factor FDG and hierarchical Archimedean copulas. The dominance of these models is most striking over the interval of the financial market crisis, where the quality of the best Student class model was providing a substantially poorer fit. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model based on multivariate decomposition of multiplicative – absolute values and signs – components of asset returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Even though housing markets in different areas are relatively localized, regional home prices have become closely correlated and tend to be simultaneously affected by many national economic factors. In this paper, through the dynamic copula model, we confirm that regional home price dependence is time-varying and the conventional time-invariant copulas underestimate the degree of dependence during economic expansions and recessions. In essence, the U.S. residential real estate market has become more integrated since the mid-1980s. Using the conditional copula model, we further identify how the dependence among regional housing markets evolves along with some fundamental economic factors such as unemployment rate and interest rate. These findings can help investors and home buyers to better identify and evaluate the systematic risk in the nationwide housing market. [ABSTRACT FROM AUTHOR]

We determine the lower bound for possible values of Spearman's rho of a bivariate copula given that the value of its Spearman's footrule is known and show that this bound is always attained. We also give an estimate for the exact upper bound and prove that the estimate is exact for some but not all values of Spearman's footrule. Nevertheless, we show that the estimate is quite tight. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the dependence structure between sukuk (Islamic bonds) yields and stock market (returns and volatility) in the case of Saudi Arabia. We consider three Archimedean copula models with different tail dependence structures namely Gumbel, Clayton, and Frank. This study shows that the sukuk yields exhibit significant dependence only with stock market volatility. In addition, the dependence structure between sukuk yields and stock market volatility are symmetric and linked with the same intensity.

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the development and application are still in infancy. Two broad branches of integration of the two concepts, entropy copula and copula entropy, are introduced in this study. On the one hand, the entropy theory can be used to derive new families of copulas based on information content matching. On the other hand, the copula entropy provides attractive alternatives in the nonlinear dependence measurement even in higher dimensions. We introduce in this study the integration of entropy and copula theories in the dependence modeling and analysis to illustrate the potential applications in hydrology and water resources.