ON ORDER STATISTICS FROM DISCRETE VARIABLES

Öz

In this study, joint pf and df of any p order statistics of innid discrete random variables are expressed in several form of integral. Also, expressions connecting distributions of order statistics of innid discrete random variables to that of order statistics of iid discrete random variables are obtained. Finally, some results related to pf and df of the order statistics are given.

Anahtar Kelimeler

• Permanent,Order Statistics,Distribution Function,Probability Function,Discrete Random Variable

Kaynakça

1. [1] Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N., (1992). A first course in Order Statistics. John Wiley and Sons Inc., New York.
2. [2] Balakrishnan, N., (1986). Order Statistics from Discrete Distributions. Commun. Statist. Theor. Meth. 15, 657-675.
3. [3] Balakrishnan, N., (2007). Permanents, order statistics, outliers and robustness. Rev. Mat. Complut. 20, 7-107.
4. [4] Balasubramanian, K. and Beg, M.I., (2003). On special linear identities for order statistics. Statistics 37, 335-339.
5. [5] Balasubramanian, K., Beg, M.I., and Bapat, R.B., (1991). On families of Distributions Closed Under Extrema. Sankhyā Ser. A 53, 375-388.
6. [6] Balasubramanian, K., Beg, M.I., and Bapat, R.B., (1996). An Identity for the Joint Distribution of Order Statistics and its Applications. J. Statist. Plann. Inference 55, 13-21.
7. [7] Balasubramanian, K., Balakrishnan, N., and Malik, H.J., (1994). Identities for Order Statistics from Non-Independent Non- Identical Variables. Sankhyā Ser. B 56, 67-75.
8. [8] Bapat, R.B. and Beg, M.I., (1989). Order Statistics for Nonidentically Distributed Variables and Permanents. Sankhyā Ser. A 51, 79-93.

9. [9] Beg, M.I., (1991). Recurrence Relations and Identities for Product Moments of Order Statistics Corresponding to Nonidentically Distributed Variables. Sankhyā Ser. A 53, 365-374.
10. [10] Cao, G. and West, M., (1997). Computing Distributions of Order Statistics. Communications in Statistics Theory and Methods 26, 755-764.
11. [11] Childs, A. and Balakrishnan, N., (2006). Relations for Order Statistics from Non-Identical Logistic Random Variables and Assessment of The Effect of Multiple Outliers on Bias of Linear Estimators. Journal of Statistical Planning and Inference 136, 2227-2253.
12. [12] Corley, H.W., (1984). Multivariate Order Statistics. Commun. Statist. Theor. Meth. 13, 1299-1304.
13. [13] Cramer, E., Herle, K., and Balakrishnan, N., (2009). Permanent Expansions and Distributions of Order Statistics in the INID Case. Communications in Statistics - Theory and Methods 38, 2078-2088.
14. [14] David, H.A., (1981). Order Statistics. John Wiley and Sons Inc., New York.
15. [15] Gan, G. and Bain, L.J., (1995). Distribution of order statistics for discrete parents with applications to censored sampling. J. Statist. Plann. Inference 44, 37-46.
16. [16] Goldie, C.M. and Maller, R.A., (1999). Generalized Densities of Order Statistics. Statistica Neerlandica 53, 222-246.
17. [17] Guilbaud, O., (1982). Functions of non-i.i.d. Random Vectors Expressed as Functions of i.i.d. random vectors. Scand. J. Statist. 9, 229-233.
18. [18] Khatri, C.G., (1962). Distributions of Order Statistics for Discrete Case. Annals of the Ins. of Stat. Math. 14,167-171.
19. [19] Nagaraja, H.N., (1986). Structure of Discrete Order Statistics. J. Statist. Plann. Inference 13, 165-177.
20. [20] Nagaraja, H.N., (1992). Order Statistics from Discrete Distributions. Statistics 23, 189-216.
21. [21] Reiss, R.D., (1989). Approximate distributions of order statistics. Springer-Verlag, New York.
22. [22] Vaughan, R.J. and Venables, W.N., (1972). Permanent Expressions for Order Statistics Densities, Journal of the Royal Statistical Society Ser. B 34, 308-310.