Öz
In this study, the probability density function(pdf) and distribution function(df) of the rth order statistics arising from independent but not necessarily identically distributed(innid) continuous random variables are expressed. Then, the results related to distributions of minimum and maximum order statistics of innid continuous random variables are given.
Kaynakça
- B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, 1992, A first course in order statistics, John Wiley and Sons Inc., New York.
- N. Balakrishnan, 2007, Permanents, order statistics, outliers and robustness, Rev. Mat. Complut. 20, no.1, 7-107.
- K. Balasubramanian and M. I. Beg, 2003, On special linear identities for order statistics, Statistics 37, no.4, 335-339.
- K. Balasubramanian, M. I. Beg and R. B. Bapat, 1991, On families of distributions closed under extrema, Sankhy: Ser. A 53, no.3, 375-388.
- K. Balasubramanian, M. I. Beg and R. B. Bapat, 1996, An identity for the joint distribution of order statistics and its applications, J. Statist. Plann. Inference 55, no.1, 13-21.
- K. Balasubramanian, N. Balakrishnan and H. J. Malik, 1994, Identities for order statistics from non- independent non- identical variables, Sankhy: Ser. B 56, no.1, 67-75.
- R. B. Bapat and M. I. Beg, 1989, Order statistics for nonidentically distributed variables and permanents, Sankhy: Ser. A 51, no.1, 79-93.
- M. I. Beg, 1991, Recurrence relations and identities for product moments of order statistics corresponding to nonidentically distributed variables, Sankhy: Ser. A 53, no.3, 365-374.
- G. Cao and M. West, 1997, Computing distributions of order statistics, Communications in Statistics Theory and Methods 26, no.3, 755-764.
- A. Childs and N. Balakrishnan, 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, no.7, 2227-2253.
- H. W. Corley, 1984, Multivariate order statistics, Commun. Statist.- Theor. Meth. 13, no.10, 1299-1304.
- E. Cramer, K. Herle and N. Balakrishnan, 2009, Permanent Expansions and Distributions of Order Statistics
- in the INID Case, Communications in Statistics - Theory and Methods 38, no.12, 2078-2088
- H. A. David, 1981, Order statistics, John Wiley and Sons Inc., New York.
- G. Gan and L. J. Bain, 1995, Distribution of order statistics for discrete parents with applications to
- censored sampling, J. Statist. Plann. Inference 44, no.1, 37-46
- C. M. Goldie and R. A. Maller, 1999, Generalized densities of order statistics, Statistica Neerlandica 53, no.2, 222-246
- O. Guilbaud, 1982, Functions of non-i.i.d. random vectors expressed as functions of i.i.d. random vectors,
- Scand. J. Statist. 9, no.4, 229-233
- C. G. Khatri, 1962, Distributions of order statistics for discrete case, Annals of the Ins. of Stat. Math. 14, no.1, 167-171
- R. -D. Reiss, 1989, Approximate distributions of order statistics, Springer-Verlag, New York.
- R. J. Vaughan and W. N. Venables, 1972, Permanent expressions for order statistics densities, Journal of
- the Royal Statistical Society Ser. B 34, no.2, 308-310 . . . . . .
Öz
Bu çalışmada, bağımsız fakat aynı dağılımlı olması gerekmeyen sürekli tesadüfi değişkenlerin artan r-inci sıralı istatistiklerinin dağılım fonksiyonu ve olasılık yoğunluk fonksiyonu ifade edildi. Bağımsız fakat aynı dağılımlı olması gerekmeyen sürekli tesadüfi değişkenlerin sıralı istatistiklerinin maksimum ve minimum dağılımlarıyla ilgili sonuçlar verildi.
Anahtar Kelimeler
Sıralı istatistikler Permanent Sürekli tesadüfi değişken Olasılık yoğunluk fonksiyonu Dağılım fonksiyonu.
Kaynakça
- B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, 1992, A first course in order statistics, John Wiley and Sons Inc., New York.
- N. Balakrishnan, 2007, Permanents, order statistics, outliers and robustness, Rev. Mat. Complut. 20, no.1, 7-107.
- K. Balasubramanian and M. I. Beg, 2003, On special linear identities for order statistics, Statistics 37, no.4, 335-339.
- K. Balasubramanian, M. I. Beg and R. B. Bapat, 1991, On families of distributions closed under extrema, Sankhy: Ser. A 53, no.3, 375-388.
- K. Balasubramanian, M. I. Beg and R. B. Bapat, 1996, An identity for the joint distribution of order statistics and its applications, J. Statist. Plann. Inference 55, no.1, 13-21.
- K. Balasubramanian, N. Balakrishnan and H. J. Malik, 1994, Identities for order statistics from non- independent non- identical variables, Sankhy: Ser. B 56, no.1, 67-75.
- R. B. Bapat and M. I. Beg, 1989, Order statistics for nonidentically distributed variables and permanents, Sankhy: Ser. A 51, no.1, 79-93.
- M. I. Beg, 1991, Recurrence relations and identities for product moments of order statistics corresponding to nonidentically distributed variables, Sankhy: Ser. A 53, no.3, 365-374.
- G. Cao and M. West, 1997, Computing distributions of order statistics, Communications in Statistics Theory and Methods 26, no.3, 755-764.
- A. Childs and N. Balakrishnan, 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, no.7, 2227-2253.
- H. W. Corley, 1984, Multivariate order statistics, Commun. Statist.- Theor. Meth. 13, no.10, 1299-1304.
- E. Cramer, K. Herle and N. Balakrishnan, 2009, Permanent Expansions and Distributions of Order Statistics
- in the INID Case, Communications in Statistics - Theory and Methods 38, no.12, 2078-2088
- H. A. David, 1981, Order statistics, John Wiley and Sons Inc., New York.
- G. Gan and L. J. Bain, 1995, Distribution of order statistics for discrete parents with applications to
- censored sampling, J. Statist. Plann. Inference 44, no.1, 37-46
- C. M. Goldie and R. A. Maller, 1999, Generalized densities of order statistics, Statistica Neerlandica 53, no.2, 222-246
- O. Guilbaud, 1982, Functions of non-i.i.d. random vectors expressed as functions of i.i.d. random vectors,
- Scand. J. Statist. 9, no.4, 229-233
- C. G. Khatri, 1962, Distributions of order statistics for discrete case, Annals of the Ins. of Stat. Math. 14, no.1, 167-171
- R. -D. Reiss, 1989, Approximate distributions of order statistics, Springer-Verlag, New York.
- R. J. Vaughan and W. N. Venables, 1972, Permanent expressions for order statistics densities, Journal of
- the Royal Statistical Society Ser. B 34, no.2, 308-310 . . . . . .
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2010 |
| Yayımlandığı Sayı | Yıl 2010 Cilt: 3 Sayı: 2 |