Ordering and aging properties of systems with dependent components governed by the Archimedean copula

Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$ -out-of- $n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.

Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data.

Archimedean Copulas and Several Methods on Constructing Generators

The main aim of this paper is to propose new methods in constructing generators for Archimedean copulas (AC). After reviewing some construction methods of AC generators, three general methods are proposed to construct new generators. These new methods are based on any convex and decreasing functions on [0; 1] and for these forms several examples are provided.

Simulation techniques of Archimedean Copula Estimators: Parametric and Semi-Parametric Approaches

In this paper, we look at two different approaches methodologies for copula estimation. The first is based on a parametric approach using MLE and IFM methods, while the second is entirely based on Kendall's tau and spearman's rho in a semi-parametric context, where the margins are estimated non-parametrically. Interestingly, based on R software simulation techniques, the contribution of their algorithms, approach, and illustration was our main focus for this paper. As an application, a class of Archimedean copulas was notably chosen. This particular class of copulas was also presented for censored data to show the estimator's performance even better.

Modeling the Dependence of Losses of a Financial Portfolio Using Nested Archimedean Copulas

In financial analysis, stochastic models are more and more used to estimate potential outcomes in a risky framework. This paper proposes an approach of modeling the dependence of losses on securities, and the potential loss of the portfolio is divided into sectors each including two subsectors. The Weibull model is used to describe the stochastic behavior of the default time while a nested class of Archimedean copulas at three levels is used to model the maximum of the value at risk of the portfolio.

SURVIVAL COPULA PARAMETERS ESTIMATION FOR ARCHIMEDEAN FAMILY UNDER SINGLY CENSORING

Given $(Z_{i},\delta _{i})=\left\{ \min (T_{i},C_{i}),I_{(T_{i}<C_{i})_{i=1,2}}\right\} ,$ as dependent or independent right-censored variables, general formulas are proven for a semi-parametric estimation of the proposed method. As a logical continuation of results established by N.IDIOU et al 2021 \cite{ref16}, a new estimator of $\tilde{C}$ is proposed by considering that the underlying copula is Archimedean, under singly censoring data. As an application, two Archimedean copulas models have been chosen to illustrate our theoretical results. A simulation study follows, which sheds light on the behavior of the process estimation method shown that the proposed estimator performs well in terms of relative bias and RMSE. The methodology of the proposed estimator is also illustrated by using lifetime data from the Diabetic Retinopathy Study, where its efficiency and robustness are observed.

A Study on Modelling of Bivariate Competing Risks with Archimedean Copulas

In this study we consider Archimedean copula functions to obtain estimates of cause-specific distribution functions in bivariate competing risks set up. We assume that two failure times of the same group are dependent and this dependency can be modeled by an Archimedean copula. Based on the Archimedean copula which gives best fit to the competing risk data with independent censoring we obtain the estimates of cause specific sub distributions.

Compound Archimedean Copulas

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.

Matrix-Tilted Archimedean Copulas

The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this copula construction are discussed and a further extension outlined.