Single and Product Moments of Generalized Order Statistics from Exponentiated Fréchet Distribution and a Characterization

10.6186/IJIMS.2011.22.3.2

Devendra Kumar

Generalized order statistics ； record values ； single and product moment ； recurrence relations ； exponentiated Fréchet distribution ； characterization

International Journal of Information and Management Sciences

22：3（2011 / 09 / 01）

221 - 232

英文

In this paper explicit expression and recurrence relations are derived from single and product moments of generalized order statistics from exponentiated Fréchet distribution. Further particular cases of ordinary order statistics and k-th record values are discussed and a characterization of exponentiated Fréchet distribution has been obtained on using a recurrence relation for single moments.

1. Abd-Elfattah, A. M.,Omima, A. M.(2009).Estimation of the unknown parameters of the generalized Fréchet distribution.Journal of Applied Science Research,5,1398-1408.
2. Ahmad, A. A.(2007).Relations for single and product moments of generalized order statistics from doubly truncated Burr type XII distribution.Journal of Egyptian. Mathematical. Society,15,117-128.
3. Ahmad, A. A.,Fawzy, M.(2003).Recurrence relations for single moments of generalized order statistics from doubly truncated distribution.Journal Statistical Planning and Inference,117,241-249.
4. Ahsanullah, M.(2000).Generalized order statistics from exponential distribution.Journal Statistical Planning and Inference,85,85-91.
5. Balakrishnan, N.(ed.),Rao, C. R.(ed.)(1998).Hand book of statistics.Amsterdam:North-Holand.
6. Balakrishnan, N.,Cohan, A. C.(1991).Order Statistics & Inference: Estimation Methods.San Diego:Academic Press.
7. Cramer, E.,Kamps, U.(2000).Relations for expectations of functions of generalized order statistics.Journal Statistical Planning and Inference,89,79-89.
8. Grunzien, Z.,Szynal, D.(1997).Characterization of uniform and exponential distributions via moments of the record values with random indices.Applied Statistical Sciences,5,259-266.
9. Hwang, J. S.,Lin, G. D.(1984).On a generalized moments problem II.Proc. American Mathematical Society,91,577-580.
10. Kamps, U.(1995).A Concept of generalized order statistics.Journal Statistical Planning and Inference,48,1-23.
11. Kamps, U.,Cramer, E.(2001).On distributions of generalized order statistics.Statistics,35,269-280.
12. Kamps, U.,Gather, U.(1997).Characteristic property of generalized order statistics for exponential distribution.Applied Mathematics,24,383-391.
13. Keseling, C.(1999).Conditional distributions of generalized order statistics and some characterizations.Metrika,49,27-40.
14. Khan, R. U.,Anwar, Z.,Ather, H.(2007).Recurrence relations for single and product moments of generalized order statistics from doubly truncated weibull distribution.Aligarh Journal of Statistics,27,69-79.
15. Khan, R. U.,Kumar, D.,Athar, H.(2010).Moments of generalized order statistics from Erlangtruncated exponential distribution and its characterization.International Journal of Statistics and Systems,5,455-464.
16. Kotz, S.,Nadarajah, S.(2000).Extreme value distributions: Theory and applications.London:Imperial College Press.
17. Nadarajah, S.,Kotz, S.(2003).The exponentiated Fréchet distribution.Interstat Electronic Journal,2003
18. Pawlas, P.,Szynal, D.(1998).Relations for single and product moments of the record values from exponential and Gurnbel distributions.Journal of Aoolied Statistical Sciences,7,53-61.
19. Pawlas, P.,Szynal, D.(1999).Recurrence relations for single and product moments of k-th record values from Pareto, generalized Pareto and Burr distributions.Communication of Statistics Theory and Methods,28,1699-1709.
20. Pawlas, P.,Szynal, D.(2001).Recurrence relations for single and product moments of generalized order statistics from Pareto, generalized Pareto, and Butt distributions.Communication of Statistics Theory and Methods,30,739-746.
21. Shawky, A. I.,Bakoban, R. A.(2008).Characterization from exponentiated gamma distribution based on record values.Journal of Statistical Theory and Application,7,263-277.