Previous |  Up |  Next

Article

Keywords:
copula; dependence; FGM family; measure of association
Summary:
In this paper, we study a general structure for the so-called Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions. Through examples we show how to use the proposed structure to study dependence properties of the FGM type distributions by a general approach.
References:
[1] Amblard, C., Girard, S.: Symmetry and dependence properties within a semiparametric family of bivariate copulas. J. Nonparametric Stat. 14 (2002), 715-727. DOI 10.1080/10485250215322 | MR 1941711 | Zbl 1019.62046
[2] Amblard, C., Girard, S.: A new extension of bivariate FGM copulas. Metrika 70 (2009), 1-17. DOI 10.1007/s00184-008-0174-7 | MR 2506497
[3] Bairamov, I., Kotz, S.: Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions. Metrika 56 (2002), 55-72. DOI 10.1007/s001840100158 | MR 1922211
[4] Bairamov, I., Kotz, S., Bekçi, M.: New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. J. Appl. Stat. 28 (2001), 521-536. DOI 10.1080/02664760120047861 | MR 1836732 | Zbl 0991.62032
[5] Bairamov, I., Kotz, S., Gebizlioglu, O. L.: The Sarmanov family and its generalization. S. Afr. Stat. J. 35 (2001), 205-224. MR 1910896 | Zbl 1009.62011
[6] Baker, R.: An order-statistics-based method for constructing multivariate distributions with fixed marginals. J. Multivariate Anal. 99 (2008), 2312-2327. DOI 10.1016/j.jmva.2008.02.019 | MR 2463391 | Zbl 1151.62045
[7] Church, J. D., Harris, B.: The estimation of reliability from stress-strength relationships. Technometrics 12 (1970), 49-54. DOI 10.1080/00401706.1970.10488633 | Zbl 0195.20001
[8] David, H. A., Nagaraja, H. N.: Order Statistics. Wiley Series in Probability and Statistics John Wiley & Sons, Chichester (2003). MR 1994955 | Zbl 1053.62060
[9] Drouet-Mari, D., Kotz, S.: Correlation and Dependence. Imperial College Press London (2001). Zbl 0977.62004
[10] Farlie, D. J. G.: The performance of some correlation coefficients for a general bivariate distribution. Biometrika 47 (1960), 307-323. DOI 10.1093/biomet/47.3-4.307 | MR 0119312 | Zbl 0102.14903
[11] Fisher, M., Klein, I.: Constructing generalized FGM copulas by means of certain univariate distributions. Metrika 65 (2007), 243-260. DOI 10.1007/s00184-006-0075-6 | MR 2288062
[12] Gumbel, E. J.: Bivariate exponential distributions. J. Am. Stat. Assoc. 55 (1960), 698-707. DOI 10.1080/01621459.1960.10483368 | MR 0116403 | Zbl 0099.14501
[13] Han, K. H.: A new family of negative quadrant dependent bivariate distributions with continuous marginals. Journal of the Chungcheong Mathematical Society 24 (2011), 795-805.
[14] Hlubinka, D., Kotz, S.: The generalized FGM distribution and its application to stereology of extremes. Appl. Math., Praha 55 (2010), 495-512. DOI 10.1007/s10492-010-0020-x | MR 2737716 | Zbl 1223.62080
[15] Huang, J. S., Kotz, S.: Modifications of the Farlie-Gumbel-Morgenstern distributions. A tough hill to climb. Metrika 49 (1999), 135-145. DOI 10.1007/s001840050030 | MR 1729905 | Zbl 1093.62514
[16] Lai, C. D., Xie, M.: A new family of positive quadrant dependent bivariate distributions. Stat. Probab. Lett. 46 (2000), 359-364. DOI 10.1016/S0167-7152(99)00122-4 | MR 1743993 | Zbl 0943.62043
[17] Mirhoseini, 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. Stat. Theory Appl. 10 (2011), 455-468. MR 2868281
[18] Morgenstern, D.: Einfache Beispiele zweidimensionaler Verteilungen. German Mitt.-Bl. Math. Statistik 8 (1956), 234-235. MR 0081575 | Zbl 0070.36202
[19] Nelsen, R. B.: An Introduction to Copulas. Springer Series in Statistics Springer, New York (2006). MR 2197664 | Zbl 1152.62030
[20] Rodríguez-Lallena, J. A., Úbeda-Flores, M.: A new class of bivariate copulas. Stat. Probab. Lett. 66 (2004), 315-325. DOI 10.1016/j.spl.2003.09.010 | MR 2045476 | Zbl 1102.62054
[21] Sklar, M.: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris French 8 (1960), 229-231. MR 0125600
Partner of
EuDML logo