Abstract
In the literature, up to now, it is common that
for Gumbel, Clayton and Frank calculated Kendall Distribution function and to the extent those applications have
been made. In this paper, we made Kendall Distribution function calculation for
Ali Mikhail Haq and Joe and in relation that simulation study. We generated
dependent gamma distribution. For dependency between these variables we used
Archimedean copula. In connection with this, we define basic properties of
copulas and their nonparametric method. In this study, to explain the
relationship between the variables, five Archimedean copula families were used;
Gumbel, Clayton, Frank Joe and Ali Mikhail Haq. We obtained nonparametric
estimation of these copula families parameters and the suitable Archimedean
copula family for this data set.
References
- [1]. Sklar. Fonctions de Repartition a n Dimensions et Leurs Marges., Publications de I’lnstitut de Statistique de I’Universite de Paris, 1959, vol 8: pp. 229-231
- [2]. Nelsen R. An Introduction to Copulas. Springer-Verlag, New York 1999.
- [3]. Genest L.P. Rivest. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 1993, 88: (423) 1034-1043.
- [4]. Genest J. MacKay.. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien 1986 40: 280-283.
- [5]. Frees E.W., Valdez E.A.Understanding relationships using copulas. North American Actuarial Journal1998. 2:1-25.
- [6]. B. Schweizer B., Wolff E.F. On nonparametric measures of dependence for random variables. Annals of Statistics 1981, 9:879-885.
- [7]. Metin A, Çalık S.,Copula Function and Application with Economic Data.. Turkish Journal of Science and Technology. 2012, Vol 7: No 2, 199-204.
- [8]. Naifar N. Modeling dependence structure with Archimedean copulas and applications to the iTraxx CDS index. Journal of Computational and Applied Mathematics. 2010 235: 2459-2466.
Abstract
Literatürde şimdiye kadar Gumbel Clayton
ve Frank arşimedyan copula aileleri için Kendall dağılım fonksiyonu
hesaplanmış ve bununla ilgili uygulamalar yapılmıştır.Bu makalede Ali Mikhail
ve Joe için Kendall dağılım fonksiyonu hesaplayarak simülasyon çalışması yaptık. Gamma dağılımından
bağımlı iki değişken ürettik.Bu değişkenler arasındaki bağımlılık yapısı için
arşimedyan copula kullandık. Bununla bağlantılı olarak copulanın temel
özelliklerini ve parametrik olmayan method tanımladık. Bu çalışmada değişkenler
arasındaki bağımlılık yapısını açıklamak için beş copula ailesi Gumbel,
Clayton, Frank Joe ve Ali Mikhail Haq ailesi kullanıldı.Bu copula ailelerinin parametrik olmayan
tahmini ve veri seti için uygun copula ailesini elde ettik.
References
- [1]. Sklar. Fonctions de Repartition a n Dimensions et Leurs Marges., Publications de I’lnstitut de Statistique de I’Universite de Paris, 1959, vol 8: pp. 229-231
- [2]. Nelsen R. An Introduction to Copulas. Springer-Verlag, New York 1999.
- [3]. Genest L.P. Rivest. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 1993, 88: (423) 1034-1043.
- [4]. Genest J. MacKay.. The joy of copulas: bivariate distributions with uniform marginal. The American Statisticien 1986 40: 280-283.
- [5]. Frees E.W., Valdez E.A.Understanding relationships using copulas. North American Actuarial Journal1998. 2:1-25.
- [6]. B. Schweizer B., Wolff E.F. On nonparametric measures of dependence for random variables. Annals of Statistics 1981, 9:879-885.
- [7]. Metin A, Çalık S.,Copula Function and Application with Economic Data.. Turkish Journal of Science and Technology. 2012, Vol 7: No 2, 199-204.
- [8]. Naifar N. Modeling dependence structure with Archimedean copulas and applications to the iTraxx CDS index. Journal of Computational and Applied Mathematics. 2010 235: 2459-2466.
Details
| Journal Section | Natural Sciences |
|---|---|
| Authors | |
| Publication Date | December 8, 2017 |
| Submission Date | March 9, 2017 |
| Acceptance Date | May 30, 2017 |
| Published in Issue | Year 2017 |