The class of bivariate Archimax copulas spans a broad range of dependence. However, its size is much reduced when the degree of association is prespecified. The extent of this reduction is studied ...for a large set of measures of association. The cases of exchangeable and non-exchangeable Archimax copulas are both considered.
In this article, we consider an expression for the probability
, where X and Y are random variables denoting the strength and stress respectively. We assume that X and Y follow two-parameter Pareto ...distributions and model their dependency by a copula with the dependency parameter θ. We obtain expression for R for four copula functions. We estimate R by plugging in the estimates of the marginal parameters and θ in its expression. The estimates of the marginal parameters are based on the marginal likelihoods. The estimates of θ are obtained from two different methods: one is based on the conditional likelihood and the other on the method of moments using Blomqvist's beta. Results of a simulation study show that the estimates based on Blomqvist's beta are better. We plot the graph of R versus θ to study the effect of dependency on R.
In this paper we define multivariate versions of the medial correlation coefficient and the rank correlation coefficient Spearman's footrule in terms of copulas. We also present corresponding results ...for the sample statistic and provide a comparison of lower bounds among different measures of multivariate association. PUBLICATION ABSTRACT
In this paper, we construct and characterise multivariate copulas with cubic sections in one variable. We also study some of their properties: ordering, dependence concepts, and a measure of ...multivariate association. Several examples illustrate our results.
We find pointwise best-possible bounds on the bivariate distribution function of continuous random variables with given margins and a given value of the medial correlation coefficient, and compare ...those bounds to those obtained from a given value of Kendall's tau and Spearman's rho.
We compare measures of concordance that arise as Pearson’s linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing ...distributions. The class of such transformed rank correlations includes Spearman’s rho, Blomqvist’s beta and van der Waerden’s coefficient. When only the standard axioms of measures of concordance are required, it is not always clear which transformed rank correlation is most suitable to use. To address this question, we compare measures of concordance in terms of their best and worst asymptotic variances of some canonical estimators over a certain set of dependence structures. A simple criterion derived from this approach is that concordance-inducing distributions with smaller fourth moment are more preferable. In particular, we show that Blomqvist’s beta is the optimal transformed rank correlation in this sense, and Spearman’s rho outperforms van der Waerden’s coefficient. Moreover, we find that Kendall’s tau, although it is not a transformed rank correlation of that nature, shares a certain optimal structure with Blomqvist’s beta.
In this paper, we propose a simple non-parametric goodness-of-fit test for elliptical copulas of any dimension. It is based on the equality of Kendall’s tau and Blomqvist’s beta for all bivariate ...margins. Nominal level and power of the proposed test are investigated in a Monte Carlo study. An empirical application illustrates our goodness-of-fit test at work.
A statistical procedure to determine if the dependence structure of a multivariate random vector belongs or not to the general class of elliptical copulas has been proposed by Jaser et al. (Depend ...Model 5:330–353, 2017). Their test exploits the fact that when the copula of a multivariate population is elliptical, the theoretical Kendall and Blomqvist dependence measures of each pair are the same. Under a setup where the marginal distributions are known, they based their decision rule on the asymptotic distribution of the proposed test statistic, which is chi-squared. In this paper, the restrictive assumption of known marginals is relaxed by the use of ranks. In addition, new test statistics are proposed and their p-values are computed from suitably adapted bootstrap replicates based on the form of their limit under the null hypothesis. Unlike Jaser et al.’s test, the proposed procedures keep their nominal level well when the dimension exceeds two. It is also shown that the new tests have good power properties against several types of alternatives to copula ellipticity.
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![Estimation of $$ P[Y<X] $$ ...](http://api.summon.serialssolutions.com/2.0.0/image/issn/XR4PS5YY4K/2198-5804/small "Estimation of $$ P[Y<X] $$ for Dependence of Stress–Strength Models with Weibull Marginals")
