Progressive censoring from heterogeneous distributions with applications to robustness

Annals of the Institute of Statistical Mathematics

Volumn 60, Issue 1, 2008, Pages 151-171

  Balakrishnan, N ^a   Cramer, Erhard ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Exponential distribution; Generalized order statistics; Order statistics from non identically distributed random sample; Permanents; Progressive censoring; Proportional hazards; Single outlier; Spacings

Indexed keywords

ASYMPTOTIC STABILITY; DENSITY FUNCTIONAL THEORY; PROPORTIONAL CONTROL SYSTEMS; RANDOM PROCESSES;

EXPONENTIAL DISTRIBUTION; GENERALIZED ORDER STATISTICS; PROPORTIONAL HAZARDS; SINGLE OUTLIER; SPACINGS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 39349087137     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-006-0070-8     Document Type: Article

References (33)

1. Arnold B.C., Balakrishnan N. (1989). Relations, bounds and approximations for order statistics. Lecture Notes in Statistics (Vol. 53). Springer, Berlin Heidelberg New York
2. Arnold B.C., Balakrishnan N., Nagaraja H.N. (1992). A first course in order statistics. Wiley, New York
3. Balakrishnan N. (1988). Recurrence relations for order statistics from n independent and non-identically distributed random variables. Annals of the Institute of Statistical Mathematics 40, 273-277
4. Balakrishnan N. (1989). Recurrence relations among moments of order statistics from two related sets of independent and non-identically distributed random variables. Annals of the Institute of Statistical Mathematics 41, 323-329
5. Balakrishnan N. (1994). Order statistics from non-identical exponential random variables and some applications (with discussion). Computational Statistics & Data Analysis 18, 203-253
6. Balakrishnan N., Aggarwala R. (2000). Progressive censoring: theory, methods, and applications. Birkhäuser, Boston
7. Balakrishnan N., Cramer E., Kamps U. (2001). Bounds for means and variances of progressive Type II censored order statistics. Statistics & Probability Letters 54, 301-315
8. Bapat R. (1990). Permanents in probability and statistics. Linear Algebra and its Applications 127, 3-25
9. Bapat R., Beg M.I. (1989a). Identities and recurrence relations for order statistics corresponding to nonidentically distributed variables. Communications in Statistics - Theory and Methods 18, 1993-2004
10. Bapat R., Beg M.I. (1989b). Order statistics for nonidentically distributed variables and permanents. Sankhyā, Series A 51, 79-93
11. Barlow R.E., Proschan F. (1975). Statistical theory of reliability and life testing: probability models. Holt-Rinehart and Winston, New York
12. Barnett V., Lewis T. (1993) Outliers in statistical data (3rd ed.). Wiley, Chichester
13. Burkschat M., Cramer E., Kamps U. (2006). On optimal schemes in progressive censoring. Statistics & Probability Letters 76, 1032-1036
14. Cohen A.C. (1963). Progressively censored samples in life testing. Technometrics 5, 327-339
15. Cramer E., Kamps U. (2003). Marginal distributions of sequential and generalized order statistics. Metrika 58, 293-310
16. Cramer E., Kamps U., Rychlik T. (2002). Evaluations of expected generalized order statistics in various scale units. Applied Mathematics 29, 285-295
17. David H.A., Nagaraja H.N. (2003). Order statistics (3rd ed). Wiley, Hoboken
18. Gross A.J., Hunt H.H., Odeh R.E. (1986). The correlation coefficient between the smallest and largest observations when (n-1) of the n observations are i.i.d. exponentially distributed. Communications in Statistics - Theory and Methods 15, 1113-1123
19. Gupta R.C., Kirmani S.N.U.A. (1988). Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probability in Engineering and Information Sciences 2, 475-484
20. Harter H.L., Balakrishnan N. (1998). Order statistics: a historical perspective. In: Balakrishnan N., Rao C.R. (eds). Handbook of Statistics (Vol. 16) Elsevier, Amsterdam, pp. 25-64
21. Joshi P.C. (1972). Efficient estimation of the mean of an exponential distribution when an outlier is present. Technometrics 14, 137-143
22. Joshi P.C. (1988). Estimation and testing under exchangeable exponential model with a single outlier. Communications in Statistics - Theory and Methods 7, 2315-2326
23. Kale B.K., Sinha S.K. (1971). Estimation of expected life in the presence of an outlier observation. Technometrics 13, 755-759
24. Kamps U. (1995). A concept of generalized order statistics. Teubner, Stuttgart
25. Kamps U., Cramer E. (2001). On distributions of generalized order statistics. Statistics 35, 269-280
26. Kochar S.C., Kirmani S.N.U.A. (1995). Some results on normalized spacings from restricted families of distributions. Journal of Statistical Planning and Inference 46, 47-57
27. Kochar S.C., Korwar R. (1996). Stochastic orders for spacings of heterogeneous exponential random variables. Journal of Multivariate Analysis 57, 69-83
28. Kochar S.C., Rojo J. (1996). Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions. Journal of Multivariate Analysis 59, 272-281
29. Marshall A.W., Olkin I. (1979). Inequalities: theory of majorization and its applications. Academic, New York
30. Minc H. (1978). Permanents. Addison-Wesley, Reading
31. Pledger G., Proschan F. (1971). Comparisons of order statistics and of spacings from heterogeneous distributions. In: Rustagi J.S. (eds). Optimization methods in statistics. Academic, New York, pp. 89-113
32. Sen P.K. (1970). A note on order statistics for heterogeneous distributions. Annals of Mathematical Statistics 41, 2137-2139
33. Vaughan R.J., Venables W.N. (1972). Permanent expressions for order statistic densities. Journal of the Royal Statistical Society, Series B 34, 308-310