Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
copula; extreme-value copula; dependence measures; distortion; competing risks
copula; extreme-value copula; dependence measures; distortion; competing risks
Summary:
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences are investigated for some special cases. Simulation results are given to examine the effectiveness of the proposed model.
References:
[1] Asgharzadeh, A., Bakouch, H. S., Nadarajah, S., Esmaeili, L.: A new family of compound lifetime distributions. Kybernetika 50 (2014), 142-169. DOI 10.14736/kyb-2014-1-0142 | MR 3195009
[2] Crane, G., Hoek, J.: Using distortions of copulas to price synthetic CDOs. Insurance Math. Econom. 42 (2008), 903-908. DOI 10.1016/j.insmatheco.2007.10.007 | MR 2435360
[3] Crowder, M. J.: Classical Competing Risks. Chapman and Hall/CRC, New York 2001. DOI 10.1201/9781420035902
[4] Dolati, A., Amini, M., Mirhosseini, S. M.: Dependence properties of bivariate distributions with proportional (reversed) hazards marginals. Metrika 77 (2014), 333-347. DOI 10.1007/s00184-013-0440-1 | MR 3175127
[5] Dolati, A., Ućbeda-Flores, M.: Constructing copulas by means of pairs of order statistics. Kybernetika 45 (2009), 992-1002. MR 2650078
[6] Durante, F.: Construction of non-exchangeable bivariate distribution functions. Statist. Papers 50 (2009), 383-391. DOI 10.1007/s00362-007-0064-5 | MR 2476195
[7] Durante, F., Foschi, R., Sarkoci, P.: Distorted copulas: constructions and tail dependence. Commun. Statistics-Theory Methods 39 (2010), 2288-2301. DOI 10.1080/03610920903039506 | MR 2755652 | Zbl 1194.62075
[8] Durrleman, V., Nickeghbali, A., Roncalli, T.: A simple transformation of copulas. Available at: gro.creditlyonnais.fr/content/rd/home copulas.htm, (2000).
[9] Genest, C., Rivest, L.: On the multivariate probability integral transformation. Statist. Probab. Lett. 53 (2001), 391-399. DOI 10.1016/s0167-7152(01)00047-5 | MR 1856163
[10] Goldoust, M., Rezaei, S., Si, Y., Nadarajah, S.: A lifetime distribution motivated by parallel and series structures. Commun. Statistics-Theory Methods 47 (2017), 3052-3072. DOI 10.1080/03610926.2017.1346802 | MR 3804208
[11] Goudendorf, G., Segers, J.: Extreme Value Copulas. In: Copula Theory and Its Applications, Lecture Notes in Statistics (P. Jaworski, F. Durante, W. Härdle, T. Rychlik, eds.), Springer, Berlin, Heidelberg 2010, 198, pp. 127-145. DOI 10.1007/978-3-642-12465-5_6 | MR 3051266
[12] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall-London, Berlin 1997. DOI 10.1002/(sici)1097-0258(19980930)17:18<2154::aid-sim913>3.0.co;2-r | MR 1462613 | Zbl 0990.62517
[13] Kotz, S., Nadarajah, S.: Extreme-Value Distributions: Theory and Applications. Imperial College Press-London, Berlin 2001. DOI 10.1142/9781860944024 | MR 1892574
[14] Kotz, S., Lumelskii, Y., Pensky, M.: The Stress-Strength Models and its Generalizations. World Scientific Publishing-Singapore, Berlin 2003. DOI 10.1142/5015 | MR 1980497
[15] Kundu, D., Gupta, A.: On bivariate Weibull-geometric distribution. J. Multivariate Anal. 123 (2014), 19-29. DOI 10.1016/j.jmva.2013.08.004 | MR 3130418
[16] Li, C., Li, X.: Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components. Metrika 81 (2018), 4, 445-464. DOI 10.1007/s00184-018-0651-6 | MR 3795184
[17] Lu, Y.: The distribution of unobserved heterogeneity in competing risks models. Statist. Papers (2017). DOI 10.1007/s00362-017-0956-y
[18] Marshall, A. W., Olkin, I.: A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84 (1997), 641-652. DOI 10.1093/biomet/84.3.641 | MR 1603936 | Zbl 0888.62012
[19] Mirhosseini, S. M., Dolati, A., Amini, M.: On a class of distributions generated by stochastic mixture of the extreme order statistics of a sample of size two. J. Statist. Theory Appl. 10 (2011), 455-468. MR 2868281
[20] Mirhosseini, S. M., Amini, M., Dolati, A.: On a general structure of the bivariate FGM type distributions. Appl. Math. 60 (2015), 91-108. DOI 10.1007/s10492-015-0086-6 | MR 3299874
[21] Morillas, P.: A method to obtain new copulas from a given one. Metrika 61 (2005), 169-184. DOI 10.1007/s001840400330 | MR 2159414
[22] Nelsen, R. B.: An Introduction to Copulas. Springer Science and Business Media, 2006. DOI 10.1007/0-387-28678-0 | MR 2197664 | Zbl 1152.62030
[23] Pikhands, J.: Multivariate extreme-value distributions (with a discussion). In: Proc. 43rd session of the International Statistical Institute. Bull. Int. Inst. 49 (1981), pp. 859-878. MR 0820979
[24] Popović, B. V., Genç, A. İ.: On extremes of two-dimensional Student-t distribution of the Marshall-Olkin type. Mediter. J. Math. 15 (2018), 4, Article: 153. DOI 10.1007/s00009-018-1201-1 | MR 3814571
[25] Roozegar, R., Jafari, A. A.: On bivariate generalized linear failure rate-power series class of distributions. Iran. J. Science Technol., Trans. A: Science 41 (2017), 693-706. DOI 10.1007/s40995-017-0297-7 | MR 3714812
[26] Roozegar, R., Nadarajah, S.: New classes of power series bivariate copulas. J. Comput. Appl. Math. 326 (2017), 235-246. DOI 10.1016/j.cam.2017.05.020 | MR 3668573
[27] Shih, J. H., Emura, T.: Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula. Statist. Papers (2016). DOI 10.1007/s00362-016-0865-5 | MR 4008679
[28] Sklar, A.: Function de repartition an dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-331. MR 0125600
[29] Zhang, K., Lin, J., Xu, P.: A new class of copulas involving geometric distribution: Estimation and applications. Insurance: Mathematics and Economics 66 (2016), 1-10. DOI 10.1016/j.insmatheco.2015.09.008 | MR 3435782
Search
Partner of
