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A new class of copulas involving geometric distribution: Estimation and applications

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  • Zhang, Kong-Sheng
  • Lin, Jin-Guan
  • Xu, Pei-Rong

Abstract

Copula is becoming a popular tool for modeling the dependence structure among multiple variables. Commonly used copulas are Gaussian, t and Gumbel copulas. To further generalize these copulas, a new class of copulas, referred to as geometric copulas, is introduced by adding geometric distribution into the existing copulas. The interior-point penalty function algorithm is proposed to obtain maximum likelihood estimation of the parameters of geometric copulas. Simulation studies are carried out to evaluate the efficiency of the proposed method. The proposed estimation method is illustrated with workers’ compensation insurance data and exchange rate series data.

Suggested Citation

  • Zhang, Kong-Sheng & Lin, Jin-Guan & Xu, Pei-Rong, 2016. "A new class of copulas involving geometric distribution: Estimation and applications," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 1-10.
    • Handle: RePEc:eee:insuma:v:66:y:2016:i:c:p:1-10
    DOI: 10.1016/j.insmatheco.2015.09.008
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    References listed on IDEAS

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    1. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2012. "Statistical Inferences for Generalized Pareto Distribution Based on Interior Penalty Function Algorithm and Bootstrap Methods and Applications in Analyzing Stock Data," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 173-193, February.
    2. Edward Frees & Virginia Young & Yu Luo, 2001. "Case Studies Using Panel Data Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(4), pages 24-42.
    3. Gregor Weiß, 2011. "Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study," Computational Statistics, Springer, vol. 26(1), pages 31-54, March.
    4. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    5. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    7. Zhang, Ran & Czado, Claudia & Min, Aleksey, 2011. "Efficient maximum likelihood estimation of copula based meta t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1196-1214, March.
    8. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    9. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    10. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
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