Tail dependence for skew Laplace distribution and skew Cauchy distribution

ABSTRACT

Coefficient of tail dependence measures the strength of dependence in the tail of a bivariate distribution and it has been found useful in the risk management. In this paper, we derive the upper tail dependence coefficient for a random vector following the skew Laplace distribution and the skew Cauchy distribution, respectively. The result shows that skew Laplace distribution is asymptotically independent in upper tail, however, skew Cauchy distribution has asymptotic upper tail dependence.

Keywords:

• Asymptotic tail dependence
• Copula
• Generalized asymmetric Laplace distribution
• Skew Cauchy distribution
• Variance–mean mixture

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60G15
• Secondary: 60G70

Acknowledgments

The authors would like to thank the Editor-in-Chief and the referee for carefully reading the paper and for their comments which greatly improved the paper.

Funding

This work was supported by the National Natural Science Foundation of China [grant number 71271227] and the Program for Innovation Team Building at Institutions of Higher Education in Chongqing [grant number KJTD201321].