Main Article Content
In multivariate survival analysis, estimating the multivariate distribution functions and then measuring the association between survival times are of great interest. Copula functions, such as Archimedean Copulas, are commonly used to estimate the unknown bivariate distributions based on known marginal functions. In this paper the feasibility of using the idea of local dependence to identify the most efficient copula model, which is used to construct a bivariate Weibull distribution for bivariate Survival times, among some Archimedean copulas is explored. Furthermore, to evaluate the efficiency of the proposed procedure, a simulation study is implemented. It is shown that this approach is useful for practical situations and applicable for real datasets. Moreover, when the proposed procedure implemented on Diabetic Retinopathy Study (DRS) data, it is found that treated eyes have greater chance for non-blindness compared to untreated eyes.
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Fisher N I. Copulas. Encyclopedia of Statistical Sciences, 2nd ed., New York, John Wiley Sons, 2006, 1363-1376.
Nelsen B. An Introduction to Copulas, 2nd ed., New York, Springer, 2006.
Genest C, MacKay J. The joy of copulas: Bivariate distributions with uniform marginal. Am Stat, 1986, 40, 280–283.
Joe H. Multivariate Models and Dependence Concepts. 1997, Chapman and Hall, London.
Henry Louie. Evaluation of bivariate Archimedean and elliptical copulas to model wind power dependency structures. Wind Energy, 2014, 17, 225-240.
Yee K C, Suhaila J, Yusof F, Mean F H. Bivariate copula in fitting rainfall data. AIP Conf Proc, 2014, 1605, 986-990.
Hofert M. Sampling Archimedean Copulas. COMPUT STAT DATA AN, 2008, 52, 5163–5174.
Embrechts P, McNeil A, Straumann D. Correlation and dependence in risk management: Properties and pitfalls. Cambridge University Press, 2002, 81, 176-223.
McNeil A J, Neslehová J. Multivariate Archimedean copulas, d-monotone functions and l-norm symmetric distributions. Ann. Statist., 2009, 37, 3059–3097.
Corbella S, Stretch D D. Simulating a multivariate sea storm using Archimedean copulas. COAST ENG J, 2013, 76, 68 -78.
Patton A J. Modeling Asymmetric Exchange rate Dependence. Int. Econ. Rev., 2006, 47, 527-556.
Chan Y, Li H. Tail dependence for multivariate t-copulas and its monotonicity. INSUR MATH ECON, 2008, 42, 763–770.
Joe H, Li H , Nikoloulopoulos A K. Tail dependence functions and vine copulas. J. Multivar. Anal., 2010, 101, 252-270.
Lee T, Modarres R, Ouarda T B M J. Data-based analysis of bivariate copula tail dependence for drought duration and severity. Hydrol. Process., 2013, 27, 1454–1463.
Lei H, Joe H. Tail order and intermediate tail dependence of multivariate copulas. J. Multivar. Anal., 2011, 102, 1454–1471.
Lee E J, Kim C H, Lee S H. Life expectancy estimate with bivariate Weibull distribution using Archimedean copula. IJBB, 2011, 5, 149-161.
Esa S, Dimitro B. Dependence Structures in Politics and in Reliability. IEEE Conference Publication, 2016, 318-322.
Huster W J, Brookmeyer R, Self S G. Modelling Paired Survival Data with Covariates. Biometrics, 1989, 45, 145-156.