Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A NEW FAMILY OF NEGATIVE QUADRANT DEPENDENT BIVARIATE DISTRIBUTIONS WITH CONTINUOUS MARGINALS

  • Received : 2011.08.25
  • Accepted : 2011.12.01
  • Published : 2011.12.30
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Abstract

In this paper, we study a family of continuous bivariate distributions that possesses the negative quadrant dependence property and the generalized negatively quadrant dependent F-G-M copula. We also develop the partial ordering of this new parametric family of negative quadrant dependent distributions.

Keywords

References

  1. A. M. Ahmed, N. A. Langberg, and F. Proschan, The ordering of negative quadrant dependence, Techincal Report 786 Florida State University, 1979.
  2. R. D. Cook and M. E. Johnson, Generalized Burr-Pareto-Logistic distributions with applications to a uranium exploration data set, Technometrics 28 (1986), 123-131. https://doi.org/10.1080/00401706.1986.10488113
  3. J. Dela horra and C. Fernandez, Sensitivity to prior independence via Farlie Gumbel-Morgenstern model, Comm. Stat. Theory Methods 24 (1955), 987-996.
  4. N. Ebrahimi, The ordering of negative quadrant dependence, Comm. Statist. Theor. Meth. 11 (1982), 2389-2399. https://doi.org/10.1080/03610928208828397
  5. D. J. G. Farlie, The performance of some correlation coeffcient for a general bivariate distribution, Biometrika 47 (1960), 307-323. https://doi.org/10.1093/biomet/47.3-4.307
  6. E. H. Gumbel, Bivariate exponential distributions, J. Amer. Statist. Asso. 55 (1955), 698-707.
  7. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295. https://doi.org/10.1214/aos/1176346079
  8. N. L. Johnson and Kotzs, Distributions in, Statistics : Continuous Multivariate Distributions, Wiley, New York, 1972.
  9. C. M. Lai and M. Xie, A new family of positive quadrant dependent bivariate distributions, Statist. Probab. Lett. 46 (2000), 359-364. https://doi.org/10.1016/S0167-7152(99)00122-4
  10. E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), 1137-1153. https://doi.org/10.1214/aoms/1177699260
  11. Morgenstern, Einfache Beispiele Zweidimensionaler Verteilungen, Mitt. fur Math. Statist. 8 (1956), 234-235.
  12. R. B. Nelsen, An Introduction to Copulas, Springer, New York, 1999.
  13. H. D. Tolley, and J. E. Norman, Time on trial estimates with bivariate risks, Biometrika 60 (1979), 285-291.