On a general structure of the bivariate FGM type distributions

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• 作者：Sayed Mohsen Mirhosseini (1)
  Mohammad Amini (2)
  Ali Dolati (1)
  
  1. Department of Statistics ; Yazd University ; Yazd ; 89195-741 ; Iran
  2. Department of Statistics ; Ordered and Spatial Data Center of Excellence ; Ferdowsi University of Mashhad ; P.O. Box 1159 ; Mashhad ; 91775 ; Iran
  
• 关键词：copula ; dependence ; FGM family ; measure of association ; 62E15 ; 62H10
• 刊名：Applications of Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：60
• 期：1
• 页码：91-108
• 全文大小：181 KB
• 参考文献：1. / C. Amblard, S. Girard: Symmetry and dependence properties within a semiparametric family of bivariate copulas. J. Nonparametric Stat. / 14 (2002), 715鈥?27. CrossRef
  2. / C. Amblard, S. Girard: A new extension of bivariate FGM copulas. Metrika / 70 (2009), 1鈥?7. CrossRef
  3. / I. Bairamov, S. Kotz: Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions. Metrika / 56 (2002), 55鈥?2. CrossRef
  4. / I. Bairamov, S. Kotz, M. Bek莽i: New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. J. Appl. Stat. / 28 (2001), 521鈥?36. CrossRef
  5. / I. Bairamov, S. Kotz, O. L. Gebizlioglu: The Sarmanov family and its generalization. S. Afr. Stat. J. / 35 (2001), 205鈥?24.
  6. / R. Baker: An order-statistics-based method for constructing multivariate distributions with fixed marginals. J. Multivariate Anal. / 99 (2008), 2312鈥?327. CrossRef
  7. / J. D. Church, B. Harris: The estimation of reliability from stress-strength relationships. Technometrics / 12 (1970), 49鈥?4. CrossRef
  8. / H. A. David, H. N. Nagaraja: Order Statistics. Wiley Series in Probability and Statistics, John Wiley & Sons, Chichester, 2003.
  9. / D. Drouet-Mari, S. Kotz: Correlation and Dependence. Imperial College Press, London, 2001. CrossRef
  10. / D. J. G. Farlie: The performance of some correlation coefficients for a general bivariate distribution. Biometrika / 47 (1960), 307鈥?23. CrossRef
  11. / M. Fisher, I. Klein: Constructing generalized FGM copulas by means of certain univariate distributions. Metrika / 65 (2007), 243鈥?60. CrossRef
  12. / E. J. Gumbel: Bivariate exponential distributions. J. Am. Stat. Assoc. / 55 (1960), 698鈥?07. CrossRef
  13. / K. H. Han: A new family of negative quadrant dependent bivariate distributions with continuous marginals. Journal of the Chungcheong Mathematical Society / 24 (2011), 795鈥?05.
  14. / D. Hlubinka, S. Kotz: The generalized FGM distribution and its application to stereology of extremes. Appl. Math., Praha / 55 (2010), 495鈥?12. CrossRef
  15. / J. S. Huang, S. Kotz: Modifications of the Farlie-Gumbel-Morgenstern distributions. A tough hill to climb. Metrika / 49 (1999), 135鈥?45. CrossRef
  16. / C. D. Lai, M. Xie: A new family of positive quadrant dependent bivariate distributions. Stat. Probab. Lett. / 46 (2000), 359鈥?64. CrossRef
  17. / S. M. Mirhoseini, A. Dolati, M. Amini: 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鈥?68.
  18. / D. Morgenstern: Einfache Beispiele zweidimensionaler Verteilungen. Mitt.-Bl. Math. Statistik / 8 (1956), 234鈥?35. (In German.)
  19. / R. B. Nelsen: An Introduction to Copulas. Springer Series in Statistics, Springer, New York, 2006.
  20. / J. A. Rodr铆guez-Lallena, M. 脷beda-Flores: A new class of bivariate copulas. Stat. Probab. Lett. / 66 (2004), 315鈥?25. CrossRef
  21. / M. Sklar: Fonctions de r茅partition 脿 / n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris / 8 (1960), 229鈥?31. (In French.)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics, Fluids and Thermodynamics
  Analysis
  Mathematical and Computational Physics
  Applied Mathematics and Computational Methods of Engineering
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1572-9109

文摘

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.