 |
[email protected] |
 |
3275638434 |
 |
 |
| Paper Publishing WeChat |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
On Concomitants of Record Values from Generalized Farlie-Gumbel-Morgenstern Distribution
N. A. Mokhlis, S. K. khames
Full-Text PDF
XML 6218 Views
DOI:10.17265/2328-224X/2014.05.002
1. Faculty of Science, Ain Shams University,Cairo, Egypt. 2. University Collage for Women, Ain Shams University, Cairo, Egypt.
In this paper, we derive the distributions of concomitants of record values from generalized Farlie-Gumbel-Morgenstern family of bivariate distributions. We derive the single and the product moments of the concomitants for the general case. The results are then applied to the case of the two-parameter exponential marginal distributions. Using concomitants of record values we derive the best linear unbiased estimators of parameters of the marginal distributions. Moreover, two methods for obtaining predictors of concomitants of record values are presented. Finally, a numerical illustration is performed to highlight the theoretical results obtained.
Generalized Farlie-Gumbel-Morgenstern family, Concomitants, Record values, Best linear unbiased estimator, Best linear unbiased predictor.
Ahsanullah, M. (1980) Linear prediction of record values for the two parameter exponential distribution. Annals of the Institute of Statistical Mathematics, 32(1), 363-368.
Ahsanullah, M. (1995) Record statistics. Nova Science Publishers, Commack, New York, USA.
Ahsanullah, M. and Nevzorov , V.B. (2000) Some distributions of induced record values. Biometrical Journal, 42, 1069-1081.
Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998) Records. John Wiley and Sons, New York.
Bairamov, I., Kotz, S. and Bekci, M. (2001) New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. Journal of Applied Statistics, 28, No. 5,521-536.
Bairamov, I. G. & Kotz, S. (2002) Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions, Metrika, 56, 55-72.
Balakrishnan, N. and Lai, C.D. (2009) Continuous Bivariate Distributions. second ed. Springer. New York .
Chacko, M. and Thomas P.Y., (2006) Concomitants of record values arising from Morgenstern type bivariate logistic distribution and some of their application in parameter estimation. Metrika, 64(3), 317-331.
David, H.A. and Nagaraja, H.N. (2003) Order statistics, 3rd Edn. John Wiley and Sons, New York.
Farlie D.J.G. (1960) The performance of some correlation coefficients for a general bivariate distribution. Biometrika 47:307-323.
Goldberger, A. (1962) Best Linear Unbiased Prediction in the Generalized Linear Regression Model. Journal of the American Statistical Association, 57, 369-375.
Gumbel, E.J. (1960) Bivariate exponential distribution. Journal of the American Statistical Association, 55, 698-707.
Houchens, R.L. (1984) Record value theory and inference. Ph.D. Dissertation, University of California, Riverside, California, USA.
Huang J.S. , Kotz, S. (1984) Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71:633--636.
Huang J.S. , Kotz, S. (1999) Modifications of the Farlie-Gumbel-Morgenstern distributions. Metrika, 49, 135-145.
Johnson, N.L. and Kotz. S. (1975) On some generalized Farlie-Gumbel-Morgenstern distributions. Communications in Statistics. 4:415-427.
Johnson, N.L. and Kotz. S.(1977) On some generalized Farlie-Gumbel-Morgenstern distributions II: Regression, correlation and further generalizations. Communications in Statistics. 6:485-496.
Morgenstern, D. (1956) Einfache Beispiele zweidimensionaler Verteilungen. Mitteilungsblatt for Mathematishe Statistik 8:234-235.
Raqab, M.Z. and Ahsanullah, M. and Nevzorov, V. (2002) Concomitants of Ordered Random Variables- A Review. Journal of Statistical Theory and Applications 1, 15-26.
Wilson, J.R. (1984) Variance Reduction Techniques for Digital Simulation. American Journal of Mathematical and Management Sciences. 4(3-4), 277-312.