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In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube (0 , 1) p p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables. [ABSTRACT FROM AUTHOR]

Considering random variables X i , i = 1 , 2 , ... , n which are from dominated distributions, we divide them into { X (1) , ... , X (m) } , m ≤ n , where X (j) , j = 1 , ... , m are random vectors. Inspired by copula and Kullback-Leibler divergence, by extending probability density function to Radon-Nikodym derivative w.r.t. a σ-finite product measure, the amount DivM (X (1) , ... , X (m)) is proposed with some desirable properties to describe the essential dependence for that group of random vectors. Some examples are given to demonstrate the amount can be applied to describe the essential dependence under both continuous and discrete distributions and can capture the associations such as MTP2, POD. [ABSTRACT FROM AUTHOR]

Copula models have become one of the most popular tools, especially in finance and insurance, for modeling multivariate distributions in the past few decades, and they have recently received increasing attention for data analysis in reliability engineering and survival analysis. This paper considers two Archimedean copula models — the Gumbel-Hougaard copula and Frank copula — for analyzing one-shot device data with two correlated failure modes, which are collected from constant-stress accelerated life tests. A one-shot device is a unit that cannot be used again after a test, e.g., munitions, rockets, and automobile airbags. Only either left- or right-censored data are collected instead of the actual lifetimes of the devices under test. With the aid of Kendall's tau correlation coefficient, initial values of the dependence parameter for the copula models are presented to determine maximum likelihood estimates of model parameters through a numerical approach. Furthermore, the proposed model can be used to examine whether the correlation between times to failure modes changes over stress levels. Real data from a survival experiment are also re-analyzed to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Modeling binary familial data has been a challenging task due to the dependence among family members and the constraints imposed on the joint probability distribution of the binary responses. This paper investigates some useful familial dependence structures and proposes analyzing binary familial data using Gaussian copula model. Advantages of this approach are discussed as well as some computational details. An numerical example is also presented with an aim to show the capability of Gaussian copula model in more sophisticated data analysis. [ABSTRACT FROM AUTHOR]

Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, andk-out-of-nsystems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

The polyhazard model with dependent causes, first introduced to fit lifetime data, generalized the traditional polyhazard model by allowing the latent causes of failure to be dependent by using copula functions. When modeling lifetime data, marginal distributions are supported on the positive reals. Dropping this restriction, the method generates a rich family of univariate distributions with asymmetries and multiple modes. We show that this new family of distributions is able to approximate other distributions proposed in the literature, such as the generalized beta-generated distributions. These distributions are fitted to three real data sets. [ABSTRACT FROM AUTHOR]

Baker (2008) introduced a new class of bivariate distributions based on distributions of order statistics from two independent samples of sizen. Lin and Huang (2010) discovered an important property of Baker’s distribution and showed that the Pearson’s correlation coefficient for this distribution converges to maximum attainable value, i.e., the correlation coefficient of the Fréchet upper bound, asnincreases to infinity. Bairamov and Bayramoglu (2013) investigated a new class of bivariate distributions constructed by using Baker’s model and distributions of order statistics from dependent random variables, allowing higher correlation than that of Baker’s distribution. In this article, a new class of Baker’s type bivariate distributions with high correlation are constructed based on distributions of order statistics by using an arbitrary continuous copula instead of the product copula. [ABSTRACT FROM AUTHOR]

The copula representations for conditionally independent random variables and the distribution properties of order statistics of these random variables are studied. [ABSTRACT FROM AUTHOR]

This article answers to a problem by Kolesárová, Mesiar, and Sempi about the class of all copulas that are compatible with two given bivariate copulasAandB. It is shown that, even ifAandBare not completely dependent, the class of all copulas compatible withAandBmay consist of a singleton. [ABSTRACT FROM PUBLISHER]

We derive best-possible bounds on the class of copulas with known values at several points, under the assumption that the points are either in “increasing order” or in “decreasing order”. These bounds may be used to establish best-possible bounds on Kendall's τ and Spearman's ρ, for such copulas. An important special case is when the values of a copula are known at several diagonal points. We also use our results to establish best-possible bounds on the distribution function of the sum of two random variables with known marginal distributions when the values of the joint distribution function are known at several points. [ABSTRACT FROM AUTHOR]

Multivariate count time series data occur in many different disciplines. The class of INteger-valued AutoRegressive (INAR) processes has the great advantage to consider explicitly both the discreteness and autocorrelation characterizing this type of data. Moreover, extensions of the simple INAR(1) model to the multi-dimensional space make it possible to model more than one series simultaneously. However, existing models do not offer great flexibility for dependence modelling, allowing only for positive correlation. In this work, we consider a bivariate INAR(1) (BINAR(1)) process where cross-correlation is introduced through the use of copulas for the specification of the joint distribution of the innovations. We mainly emphasize on the parametric case that arises under the assumption of Poisson marginals. Other marginal distributions are also considered. A short application on a bivariate financial count series illustrates the model. [ABSTRACT FROM PUBLISHER]

In this article, we propose a bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo (MCMC) were considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real data. [ABSTRACT FROM PUBLISHER]

Supply chain management has received considerable attention in the literature and it is meaningful and important to be able to measure the reliability of supply chains. In the article, the suppliers in the supply chain systems are not independent of each other and the dependency relation may be either linear or nonlinear correlation. From the view of the distribution service process, a copula-based method is proposed for analyzing the reliability of supply chains. In this article, by introducing the model of k-out-of-n: G system into the studies of supply chains, an evaluation method is suggested and the reliability indexes are obtained. Finally, a numerical example is presented to illustrate the results obtained in this article. [ABSTRACT FROM AUTHOR]

One difficulty with developing multivariate attribute control charts is the lack of the related joint distribution. So, if it would be possible to generate the joint distribution of two (or more) attribute characteristics, then a bivaraite (or multivariate) attribute control chart can be developed based on Types I and II errors. Copula function is a solution to the matter. In this article, applying the copula function approach, we achieve the joint distribution of two correlated zero inflated Poisson (ZIP) distributions. Then, using this joint distribution, we develop a bivaraite control chart which can be used for monitoring correlated rare events. This copula-based bivariate ZIP control chart is compared with the simultaneous use of two separate univariate ZIP control charts. Based on the average run length (ARL) measure, it is shown that the proposed control chart is much better than the simultaneous use of two separate univariate charts. In addition, a real case study related to the environmental air in a sterilization process is investigated to show the applicability of the developed control chart. [ABSTRACT FROM AUTHOR]

We introduce and discuss a general method for constructing bivariate Archimedean copula families. The central item in our method is the function [image omitted] (t ∈ [0, 1]), where ϕ is the generator of the Archimedean copula. The construction of new copulas by means of λ has several advantages. The most important one is the straightforward relationship between the λ function and Kendall's τ and the coefficients of upper and lower tail dependence λL and λU, as defined in Joe (1997), which makes it possible to use these quantities as copula parameters and to control them independently of each other. Furthermore, the λ-method allows to construct multi-parameter families in a clear and organized way. The methodology is explained and illustrated by two- and three-parameter copula families. [ABSTRACT FROM AUTHOR]

This article presents some results showing how rectangular probabilities can be studied using copula theory. These results lead us to develop new lower and upper bounds for rectangular probabilities which can be computed efficiently. The new bounds are compared with the ones obtained from the generalized Frechet-Hoeffding bounds and Bonferroni-type inequalities. [ABSTRACT FROM AUTHOR]

In this article, we establish optimal rates for the strong approximation of empirical copula processes in 2 by sequences of Gaussian processes. These results are applied to investigate Cramer-von Mises-type statistics. [ABSTRACT FROM AUTHOR]

In survival analysis, the classical Koziol-Green random censorship model is commonly used to describe informative censoring. Hereby, it is assumed that the distribution of the censoring time is a power of the distribution of the survival time. In this article, we extend this model by assuming a general function between these distributions. We determine this function from a relationship between the observable random variables which is described by a copula family that depends on an unknown parameter θ. For this setting, we develop a semi-parametric estimator for the distribution of the survival time in which we propose a pseudo-likelihood estimator for the copula parameter θ. As results, we show first the consistency and asymptotic normality of the estimator for θ. Afterwards, we prove the weak convergence of the process associated to the semi-parametric distribution estimator. Furthermore, we investigate the finite sample performance of these estimators through a simulation study and finally apply it to a practical data set on survival with malignant melanoma. [ABSTRACT FROM AUTHOR]

A new characterization of bivariate copulas is given by using the notion of Dini derivatives. Several examples illustrate the usefulness of this result. [ABSTRACT FROM AUTHOR]

We present sharp bounds for moments of the maximum of concomitants of selected order statistics. The dependence between pair components is modeled by copulas. We use the bounds to compare some insurance premiums. [ABSTRACT FROM AUTHOR]

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion Cψ: [0, 1]2 → [0, 1], Cψ(x, y) = ψ{C[ψ-1(x), ψ-1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails. [ABSTRACT FROM AUTHOR]

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of χ2-divergence on signed finite measures. The asymptotic properties of the proposed estimate and the test statistic are studied under the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not. [ABSTRACT FROM AUTHOR]

For a truncation-invariant copula, truncation does not change the dependence structure as well as all nonparametric measures of association such as Kendall's tau and Spearman's rho. In this article, we show that the products of algebraically independent Archimedean multivariate Clayton copulas and standard uniform distributions are the only truncation-invariant copulas. [ABSTRACT FROM AUTHOR]

The limiting lower-tail dependence copula (LLTDC) is defined as the copula of random variables which are right-truncated at thresholds tending to their left endpoints. This article shows LLTDCs are truncation-invariant and belong to the Ahmadi-Clayton family. Accordingly, it follows that limiting upper-tail dependence copulas are members of the survival Ahmadi-Clayton family. [ABSTRACT FROM AUTHOR]

We consider semiparametric multivariate data models based on copula representation of the common distribution function. A copula is characterized by a parameter of association and marginal distribution functions. This parameter and the marginal distributions are unknown. In this article, we study the estimator of the parameter of association in copulas with the marginal distribution functions assumed as nuisance parameters restricted by the assumption that the components are identically distributed. Results of this work could be used to construct special kinds of tests of homogeneity for random vectors having dependent components. [ABSTRACT FROM AUTHOR]

We present a new way of constructing n-copulas, by scaling and gluing finitely many n-copulas. Gluing for bivariate copulas produces a copula that coincides with the independence copula on some grid of horizontal and vertical sections. Examples illustrate how gluing can be applied to build complicated copulas from simple ones. Finally, we investigate the analytical as well as statistical properties of the copulas obtained by gluing, in particular, the behavior of Spearman's ρ and Kendall's τ. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions are given in order to ensure that a function δ:[0, 1] → [0, 1] is the diagonal section of an absolutely continuous copula. Explicit constructions are provided. [ABSTRACT FROM AUTHOR]

This article examines a test procedure for checking the constancy of serial dependence via copulas for Markov time series data. It also provides a copula-based modeling approach for the dynamic serial dependence. Various parametric families of copulas offering different dependent structures are investigated. A score test is proposed for checking the constancy of a copula parameter. The score test is constructed and its asymptotic null distribution established under a two-stage estimation procedure. The test does not require specification of the probability distribution for the copula parameter. To capture the dynamics of dependence structure over time, autoregressive moving average and exponential type models are proposed. Illustrations are given based on simulated data and historic coffee prices data. [ABSTRACT FROM AUTHOR]

We present new tests of marginal independence for d-valued random vectors. Our tests rely upon weighted Cramér-von Mises-type statistics, which are functionals of the empirical copula process based upon a random sample of size n. We establish a decomposition of this process into asymptotically independent components, and describe the tests which follow from these arguments. [ABSTRACT FROM AUTHOR]

In multivariate and multi-parameter contexts, new expressions for Fisher Information are derived using the copula representation of the joint distribution of random variables. Invariance of Fisher Information to margins of the joint distribution is then demonstrated. [ABSTRACT FROM AUTHOR]

The problem of constructing copulas with a given diagonal section has been studied by Sungur and Yang (1996) and Fredricks and Nelsen (1997a); (b); (2002). The results of Sungur and Yang are especially relevant because, among other results, they have proven that an Archimedean copula is characterized by its diagonal section. The results obtained by Fredricks and Nelsen allow one to build a singular copula with a given a diagonal section. In all cases, the resulting copulas are symmetric. In this article, we provide a family of absolutely continuous copulas with a fixed diagonal, which can differ from another absolutely continuous copula almost everywhere with respect to Lebesgue measure. It is important to mention that the asymmetry in the proposed methodology is not an issue. [ABSTRACT FROM AUTHOR]

We consider independence tests and the methods to evaluate their efficiency. First, we observe that many of the most used independence tests are functions of the empirical copula, which is a sufficient statistic. Hence, the power of these tests, such as the tests based on Spearman's ρ, on Kendall's τ, and on Gini's γ, depend solely on the theoretical copula, and not on the marginal distributions. Then, we consider monotone dependence tests and we propose a parametric model to define the power function. Such a model is based on a path of copulas, from the copula of discordance to the copula of concordance, and can be characterized by the copula of the underlying joint distribution. Moreover, we introduce a consistent estimator of the path of copulas. Finally, we provide some examples of applications, and in particular, a bootstrap-plug-in estimator of the power curve, all useful for power comparison. [ABSTRACT FROM AUTHOR]

In this article, we define and study the concept of directional dependence in bivariate regression setting by using copulas. We consider two cases of directional dependence; one originating from marginals and the other originating from the joint behavior of variables. We also generalize and clarify the results given by Dodge and Rousson (2000) and Muddapur (2003). [ABSTRACT FROM AUTHOR]

Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Furthermore most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then provide a way to extend the construction to the n-dimensional framework. We can thus construct families of copulas in dimension n and parameterized by n - 1 parameters, implying possibly asymmetric relations. Such ‘periodic’ copulas can be simulated easily. [ABSTRACT FROM AUTHOR]

In this article we establish semiparametric density estimators by employing the ideas of copulas and density weighting functions. Results on asymptotic normality and uniform strong consistency are derived. The formula for the asymptotic mean square error is used to get the optimal bandwidth. Moreover, applications to several families of copulas are discussed. [ABSTRACT FROM AUTHOR]

If H denotes the joint distribution function of n random variables X1, X2, …, Xn whose margins are F1, F2, …, Fn, respectively, then the fundamental best-possible bounds inequality for H is max(0, Σi=1n Fi(xi) - n + 1) ≤ H(x1,x2, …,xn) ≤ min (F1(x1), F2(x2), …,Fn(xn)) for all x1, x2, …,xn in [-∞, ∞]. In this paper we employ n-copulas and n-quasi-copulas to find similar bounds on arbitrary sets of multivariate distribution functions with given margins. We discuss bounds for an n-quasi-copula Q when a value of Q at a single point is known. As an application, we investigate about bounds for a multivariate distribution function H with given univariate margins when the value of H is known at a single point whose coordinates are percentiles of the variables X1, X2, …,Xn, respectively. [ABSTRACT FROM AUTHOR]

We find maximum and minimum extensions of finite 2-subcopulas and discuss the difficulties involved in finding the least upper bound of extensions in higher dimensions. [ABSTRACT FROM AUTHOR]

We find pointwise best-possible bounds on the bivariate distribution function of continuous random variables with given margins and a given value of the population version of a nonparametric measure of association such as Kendall's tau or Spearman's rho. [ABSTRACT FROM AUTHOR]