Abstract
In the literature, up to now, it is common that for Gumbel, Clayton and Frank calculated Kendall
Distribution function K u ( ) and to the extent those applications have been made. Kendall distribution functions
show stochastic orderings of random vectors. The aim of Kendall distribution function is selected suitable copula
function for using data set. For dependence structures of the data set, we calculated Kendall Tau and Spearman
Rho values which are nonparametric. Based on this method, parameters of copula are obtained. In this paper, we
are made Kendall Distribution function which obtained with the help of generator function of Archimedean copula
calculation for Ali Mikhail Haq and Joe and in relation with that simulation study. We used data set which generated
dependent generalized pareto distribution (Gp(3,3,3)) for this study. For dependency among these variables, we
used Archimedean copula. In connection with this, we defne basic properties of copulas and nonparametric
methods Kendall Tau, Spearman Rho are given. In this study, to explain the relationship among the variables, fve
Archimedean copula are selected; Gumbel, Clayton, Frank Joe and Ali Mikhail Haq. Afterwards, we are obtained
nonparametric estimation of parameters of these copulas with the help of Kendall Tau. With Kendall distribution
function values, we found the suitable Archimedean copula family for this data set.
References
- Cherubini U, Luciano E, 2001. Value-at-risk trade-off and capital allocation with copulas. Economic Notes, 30: 235–256.
- Frees EW, Valdez EA, 1998. Understanding relationships using copulas. North American Actuarial Journal, 2: 1-25.
- Genest C, MacKay J, 1986. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien, 40: 280-283.
- Genest C, Rivest LP, 1993. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association, 88: 1034-1043.
- Genest C, Favre AC, 2006. Everything you always wanted to know about copula modelling but were afraid to ask. Journal of Hydrologic Engineering, 12: 347-368.
- Genest C, Gendron M, Boudeau-Brien M, 2009. The advent of copulas in finance. The European Journal of Finance, 15: 609-618.
- Malevergne Y, Sornette D, 2003. Testing the gaussian copula hypothesis for financial assets dependences. Quantitative Finance, 3: 231-250.
- Metin A, Çalık S, 2012. Copula function and application with economic data. Turkish Journal of Science and Technology, 7: 199-204. Naifar N, 2010. Modeling dependence structure with archimedean copulas and applications to the iTraxx CDS index. Journal of Computational and Applied Mathematics, 235: 2459-2466
- Nelsen R, 1999. An Introduction to Copulas. Springer-Verlag, New York, USA. 272p.
- Rosenberg J, Schuermann T, 2006. A general approach to integrated risk management with Skewed, Fat-tailed Risks. Journal of Financial Economics, 79: 569-614.
- Shih JH, Louis TA, 1995. Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51: 1384-1399.
- Sklar A, 1959. Fonctions de repartition a n dimensions et leurs marges. Publications de I’lnstitut de Statistique de I’University de Paris, 8: 229-231.
- Schweitzer B, Wolff EF, 1981. On nonparametric measures of dependence for random variables. Annals of Statistics, 9: 879-885.
Abstract
Literatürde şimdiye kadar Gumbel, Clayton ve Frank için Kendall dağılım fonksiyonu hesaplanmış ve
uygulamaları yapılmıştır. Kendall dağılım fonksiyonu tesadüf vektörlerin stokastik sıralamasını gösterir. Kendall
dağılım fonksiyonunun amacı kullanılan veri seti için uygun olan copula fonksiyonunu seçmektir. Veri setinin
bağımlılık yapısı için parametrik olmayan Kendall Tau ve Spearman Rho değerlerini hesapladık. Bu yönteme bağlı
olarak, copula parametreleri elde edildi. Bu çalışmada Ali Mikhail Haq ve Joe copula için arşimedyan copulanın
üreteç fonksiyonu yardımıyla Kendall dağılım fonksiyonunu hesapladık ve bununla ilgili simülasyon çalışması
yaptık. Biz bu çalışma için bağımlı genelleştirilmiş pareto (Gp(3,3,3)) dağılımından üretilen veri seti kullandık. Bu
değişkenler arasındaki bağımlılık yapısı için Arşimedyan copula kullandık. Bununla bağlantılı olarak, copulanın
temel özellikleri tanıtıldı ve nonparametrik Kendall Tau ve Spearman Rho verildi. Bu çalışmada bu değişkenler
arasındaki bağımlılık yapısını açıklamak için beş Arşimedyan copula ailesi seçildi; Gumbel, Clayton, Frank Joe ve
Ali Mikhail Haq. Devamında Kendall tau yardımıyla bu copulaların parametrelerinin nonparametrik tahmini elde
edildi. Kendall dağılım fonksiyonu değerleri ile veri seti için uygun arşimedyan copula bulundu.
References
- Cherubini U, Luciano E, 2001. Value-at-risk trade-off and capital allocation with copulas. Economic Notes, 30: 235–256.
- Frees EW, Valdez EA, 1998. Understanding relationships using copulas. North American Actuarial Journal, 2: 1-25.
- Genest C, MacKay J, 1986. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien, 40: 280-283.
- Genest C, Rivest LP, 1993. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association, 88: 1034-1043.
- Genest C, Favre AC, 2006. Everything you always wanted to know about copula modelling but were afraid to ask. Journal of Hydrologic Engineering, 12: 347-368.
- Genest C, Gendron M, Boudeau-Brien M, 2009. The advent of copulas in finance. The European Journal of Finance, 15: 609-618.
- Malevergne Y, Sornette D, 2003. Testing the gaussian copula hypothesis for financial assets dependences. Quantitative Finance, 3: 231-250.
- Metin A, Çalık S, 2012. Copula function and application with economic data. Turkish Journal of Science and Technology, 7: 199-204. Naifar N, 2010. Modeling dependence structure with archimedean copulas and applications to the iTraxx CDS index. Journal of Computational and Applied Mathematics, 235: 2459-2466
- Nelsen R, 1999. An Introduction to Copulas. Springer-Verlag, New York, USA. 272p.
- Rosenberg J, Schuermann T, 2006. A general approach to integrated risk management with Skewed, Fat-tailed Risks. Journal of Financial Economics, 79: 569-614.
- Shih JH, Louis TA, 1995. Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51: 1384-1399.
- Sklar A, 1959. Fonctions de repartition a n dimensions et leurs marges. Publications de I’lnstitut de Statistique de I’University de Paris, 8: 229-231.
- Schweitzer B, Wolff EF, 1981. On nonparametric measures of dependence for random variables. Annals of Statistics, 9: 879-885.
Details
| Primary Language | English |
|---|---|
| Journal Section | Matematik / Mathematics |
| Authors | |
| Publication Date | September 30, 2017 |
| Submission Date | April 14, 2017 |
| Acceptance Date | July 24, 2017 |
| Published in Issue | Year 2017 Volume: 7 Issue: 3 |