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The Distributions and the Moments of Concomitants of Order Statistics for Bivariate Farlie-Gumbel-Morgenstern Distributions

Year 2004, Volume: 3 Issue: 2, 1 - 11, 15.08.2004

Abstract

In this paper, the distributions and the moments of concomitants of order statistics for bivariate Farlie-Gumbel- Morgenstern (FGM) distributions are studied. Firstly, FGM distributions and their admissible range of additional parameter are given. It is shown that positive quadrant dependence property is proved for bivariate FGM distributions, and the distributions of concomnitants of order statistics are presented The distributions, the moments and the moment generating functions of concomitants of order statistics are found for uniform and exponential bivariate FGM distributions. The recurrence relations are obtained for the moments and the moment generating functions of concomitants of oder statistics.

References

  • BAIRAMOV, I. G. and BEKÇİ, M. (1999), Concomitant of Order Statistics in FGM Type Bivariate Uniform Distributions, İstatistik, Journal of the Turkish Statistical Association, 2 (2); 135-144.
  • BAIRAMOV, I., KOTZ, S. and BEKÇİ, M. (2001). New Generalized Farlie-Gumbel- Morgenstern Distributions and Concomitants of Order Statistics, J. Appl. Stat., 28 (5); 521-536.
  • BAIRAMOV, I., and ERYILMAZ, S. (2003). Characterization of Symmetry and Exceedance Multivariate FGM Distributions. Journal of Applied Statistical Science (to appear).
  • BALASUBRAMANIAN, K. and BEG, M. I. (1997). Concomitant of Order Statistics in Morgenstern Type Bivariate Exponential Distributions, Journal of Applied Statistical Science, 5 (4): 233-245.
  • BALASUBRAMANIAN, K. and BEG, M. I. (1998). Concomitant of Order Statistics in Gumbel's Bivariate Exponential Distributions, Sankhya, The Indian Journal of Statistics, 60, Series B, Pt. 3; 399-406.
  • BHATTACHARYA, P. K. (1984). Induced Order Statistics: Theory and Applications, Handbook of Statistics (P. R. Krishnaiah and P. K. Sen eds), 4; 383-403.
  • DAVID, H. A. (1981). Order Statistics, 2 nd edn., John Wiley, New York.
  • FARLIE, D. J. G. (1960), The Performance of Some Correlation Coefficients for General Bivariate Distribution, Biometrika, 47; 307-323.
  • GUMBEL, E. J. (1960), Bivariate Exponential Distributions, Journal of American Statistical Association, 55; 698-707.
  • HUANG, J. S. and KOTZ, S. (1984). Correlation Structure in Iterated Farlie-Gumbel-Morgenstern Distributions, Biometrika, 71, 633-636.
  • HUANG, J. S. and KOTZ, S. (1999). Modifications of the Farlie-Gumbel-Morgenstern Distributions. A Tough Hill to Climb, Metrika, 49; 135-145.
  • JOHNSON, N. L. and KOTZ, S. (1975), On Some Generalized Farlie-Gumbel-Morgenstern Distributions, Communications in Statistics, Theor. Meth., 4; 415-427.
  • JOHNSON, N. L. and KOTZ, S. (1977), On Some Generalized Farlie-Gumbel-Morgenstern Distributions-II: Regression, Correlations and Further Generalizations, Communications in Statistics, Theor. Meth., 6; 485-496.
  • LEHMANN, E. L. (1966), Some Concepts of Dependence, Annals of Mathematical Statistics, 37; 1137-1153.
  • MORGENSTERN, D (1956), Einfache Beispiele Zweidimensionaler Verteilungen, Mitteilungsblatt für Mathematische Statistik, 8; 234-235.
  • SCHUCANY, W. R., PARR, W. C. and BOYER, J. E. (1978), Correlation, Structure in Farlie-Gumbel-Morgenstern Distributions, Biometrika, 65 (3); 650-653.

İki Değişkenli Farlie-Gumbel-Morgenstern Dağılımları için Sıra İstatistiklerinin Eşleniklerinin Dağılımları ve Momentleri

Year 2004, Volume: 3 Issue: 2, 1 - 11, 15.08.2004

Abstract

Bu çalışmada, iki değişkenli Farlie-Gumbel-Morgenstern (FGM) dağılımları için sıra istatistiklerinin eşleniklerinin dağılımları ve momentleri çalışılmıştır. İlk olarak, FGM dağılımları ve bu dağılımların birliktelik parametresi için kabul edilebilir sınırlar verilmiştir. İki değişkenli FGM dağılımları için pozitif kadran bağımlılık özelliğinin sağlandığı gösterilmiş ve sıra istatistiklerinin eşleniklerinin dağılımları sunulmuştur. Düzgün ve Üstel tip iki değişkenli FGM dağılımları için sıra istatistiklerinin eşleniklerinin dağılımları, momentleri ve moment çıkaran fonksiyonları bulunmuştur. Sıra istatistiklerinin eşleniklerinin momentleri ve moment çıkaran fonksiyonlar için indirgeme bağıntıları elde edilmiştir.

References

  • BAIRAMOV, I. G. and BEKÇİ, M. (1999), Concomitant of Order Statistics in FGM Type Bivariate Uniform Distributions, İstatistik, Journal of the Turkish Statistical Association, 2 (2); 135-144.
  • BAIRAMOV, I., KOTZ, S. and BEKÇİ, M. (2001). New Generalized Farlie-Gumbel- Morgenstern Distributions and Concomitants of Order Statistics, J. Appl. Stat., 28 (5); 521-536.
  • BAIRAMOV, I., and ERYILMAZ, S. (2003). Characterization of Symmetry and Exceedance Multivariate FGM Distributions. Journal of Applied Statistical Science (to appear).
  • BALASUBRAMANIAN, K. and BEG, M. I. (1997). Concomitant of Order Statistics in Morgenstern Type Bivariate Exponential Distributions, Journal of Applied Statistical Science, 5 (4): 233-245.
  • BALASUBRAMANIAN, K. and BEG, M. I. (1998). Concomitant of Order Statistics in Gumbel's Bivariate Exponential Distributions, Sankhya, The Indian Journal of Statistics, 60, Series B, Pt. 3; 399-406.
  • BHATTACHARYA, P. K. (1984). Induced Order Statistics: Theory and Applications, Handbook of Statistics (P. R. Krishnaiah and P. K. Sen eds), 4; 383-403.
  • DAVID, H. A. (1981). Order Statistics, 2 nd edn., John Wiley, New York.
  • FARLIE, D. J. G. (1960), The Performance of Some Correlation Coefficients for General Bivariate Distribution, Biometrika, 47; 307-323.
  • GUMBEL, E. J. (1960), Bivariate Exponential Distributions, Journal of American Statistical Association, 55; 698-707.
  • HUANG, J. S. and KOTZ, S. (1984). Correlation Structure in Iterated Farlie-Gumbel-Morgenstern Distributions, Biometrika, 71, 633-636.
  • HUANG, J. S. and KOTZ, S. (1999). Modifications of the Farlie-Gumbel-Morgenstern Distributions. A Tough Hill to Climb, Metrika, 49; 135-145.
  • JOHNSON, N. L. and KOTZ, S. (1975), On Some Generalized Farlie-Gumbel-Morgenstern Distributions, Communications in Statistics, Theor. Meth., 4; 415-427.
  • JOHNSON, N. L. and KOTZ, S. (1977), On Some Generalized Farlie-Gumbel-Morgenstern Distributions-II: Regression, Correlations and Further Generalizations, Communications in Statistics, Theor. Meth., 6; 485-496.
  • LEHMANN, E. L. (1966), Some Concepts of Dependence, Annals of Mathematical Statistics, 37; 1137-1153.
  • MORGENSTERN, D (1956), Einfache Beispiele Zweidimensionaler Verteilungen, Mitteilungsblatt für Mathematische Statistik, 8; 234-235.
  • SCHUCANY, W. R., PARR, W. C. and BOYER, J. E. (1978), Correlation, Structure in Farlie-Gumbel-Morgenstern Distributions, Biometrika, 65 (3); 650-653.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Statistical Theory
Journal Section Research Articles
Authors

Muhammet Bekçi

Publication Date August 15, 2004
Published in Issue Year 2004 Volume: 3 Issue: 2

Cite

APA Bekçi, M. (2004). İki Değişkenli Farlie-Gumbel-Morgenstern Dağılımları için Sıra İstatistiklerinin Eşleniklerinin Dağılımları ve Momentleri. İstatistik Araştırma Dergisi, 3(2), 1-11.