scholarly journals Description of the Dependence Strength of Two Variogram Models of a Spatial Structure Using Archimedean Copulas

2017 ◽  
Vol 9 (1) ◽  
pp. 117
Author(s):  
Moumouni Diallo ◽  
Diakarya Barro
Keyword(s):  
Spatial Structure ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Variogram Models ◽  
Measure Of Similarity

Variogram is a geostatistical tool which describes how the spatialcontinuity changes with a given separating distance between pairs of stations. In this paper, we study the dependence structure within a same class of bivariate spatialized archimedean copulas. Specifically, we point out properties of the gaussian variogram and the exponential one. A new measure of similarity of two copulas is computed particularly between the spatial independent copula and full dependence one.

MODELING DEPENDENCE BETWEEN LOSS TRIANGLES WITH HIERARCHICAL ARCHIMEDEAN COPULAS

2015 ◽  
Vol 45 (3) ◽  
pp. 577-599 ◽  
Author(s):  
Anas Abdallah ◽  
Jean-Philippe Boucher ◽  
Hélène Cossette
Keyword(s):  
Life Insurance ◽  
Bootstrap Method ◽  
Dependence Structure ◽  
Insurance Company ◽  
Archimedean Copulas ◽  
Life Insurance Company ◽  
Critical Problems ◽  
Intuitive Interpretation ◽  
Property Casualty

AbstractOne of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. Recently, Shi and Frees (2011) proposed to put dependence between lines of business with a copula that captures dependence between two cells of two different runoff triangles. In this paper, we propose to generalize this model in two steps. First, by using an idea proposed by Barnett and Zehnwirth (1998), we will suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. Thereafter, we will then suppose another dependence structure that links the CYs of different lines of business. This model is done by using hierarchical Archimedean copulas. We show that the model provides more flexibility than existing models, and offers a better, more realistic and more intuitive interpretation of the dependence between the lines of business. For illustration, the model is applied to a dataset from a major US property-casualty insurer, where a bootstrap method is proposed to estimate the distribution of the reserve.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

Simulation for Mixture of Archimedean Copulas

2012 ◽  
Vol 195-196 ◽  
pp. 738-743
Author(s):  
Shi De Ou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Tail Dependence ◽  
Likelihood Estimation ◽  
Numerical Results ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Models ◽  
Random Samples ◽  
Dependence Structures

Many dependence structures can consist of mixed copulas. In order to analyze the dependence of stock, we present the method of estimation for mixed copula models. Via generating random samples and using maximum likelihood estimation, the parameters of mixture of Archimedean copulas are estimated. Numerical results show that this method estimates effectively the parameters and tail dependence coefficients. Therefore we can use the method to analyze dependence structure for stocks.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (01) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Compound Archimedean Copulas

2021 ◽  
Vol 10 (3) ◽  
pp. 126
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Copula Function ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Unique Structure ◽  
The Family ◽  
The Many

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.

STOCHASTIC ORDERING OF LIFETIMES OF PARALLEL AND SERIES SYSTEMS COMPRISING HETEROGENEOUS DEPENDENT COMPONENTS WITH GENERALIZED BIRNBAUM-SAUNDERS DISTRIBUTIONS

2020 ◽  
pp. 1-17
Author(s):  
Mehdi Amiri ◽  
Narayanaswamy Balakrishnan ◽  
Ahad Jamalizadeh
Keyword(s):  
Lower Bounds ◽  
Stochastic Ordering ◽  
Upper And Lower Bounds ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Survival Functions ◽  
Stochastic Orderings ◽  
Special Cases ◽  
Series Systems ◽  
Skew Normal

In this paper, we discuss stochastic orderings of lifetimes of two heterogeneous parallel and series systems with heterogeneous dependent components having generalized Birnbaum–Saunders distributions. The comparisons presented here are based on the vector majorization of parameters. The ordering results are established in some special cases for the generalized Birnbaum–Saunders distribution based on the multivariate elliptical, normal, t, logistic, and skew-normal kernels. Further, we use these results by considering Archimedean copulas to model the dependence structure among systems with generalized Birnbaum–Saunders components. These results have been used to derive some upper and lower bounds for survival functions of lifetimes of parallel and series systems.

scholarly journals Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

2021 ◽  
Vol 10 (5) ◽  
pp. 20
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Electricity Demand ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Maximum Daily Temperature ◽  
Multiple Parameter ◽  
Original Family ◽  
Dependence Structures

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.

scholarly journals Dependence structure of conditional Archimedean copulas

2008 ◽  
Vol 99 (3) ◽  
pp. 372-385 ◽  
Author(s):  
Mhamed Mesfioui ◽  
Jean-François Quessy
Keyword(s):  
Dependence Structure ◽  
Archimedean Copulas
Sign in / Sign up

Export Citation Format

Share Document