Progressive type II censored order statistics from exponential distributions

Statistics

Volumn 35, Issue 4, 2001, Pages 537-556

  Balakrishnan, N ^a   Cramer, E ^b   Kamps, U ^b   Schenk, N ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF OLDENBURG   (Germany)

Author keywords

Best linear unbiased estimation; Exponential distribution; Maximum likelihood estimation; Moments; Order statistics; Progressive type II censored order statistics; Truncated exponential distribution; Uniformly minimum variance unbiased estimation

Indexed keywords

EID: 0043010494     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331880108802753     Document Type: Article

References (31)

1. Aggarwala, R. and Balakrishnan, N. (1996) Recurrence relations for single and product moments of progressive type-II right censored order statistics from exponential and truncated exponential distributions. Ann. Inst. Statist. Math., 48, 757-771.
2. Aggarwala, R. and Balakrishnan, N. (1998) Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. J. Statist. Plann. Inference, 70, 35-49.
3. Balakrishnan, N. and Aggarwala, R. (2000) Progressive Censoring. Birkhäuser, Boston.
4. Balakrishnan, N., Cramer, E. and Kamps, U. (2001) Bounds for means and variances of progressive type II censored order statistics. Statist. Probab. Lett. (to appear).
5. Balakrishnan, N. and Sandhu, R. A. (1995) Linear estimation under censoring and inference. In: Balakrishnan, N. and Basu, A. P. (Eds.), The Exponential Distribution, pp. 53-72. Gordon and Breach, Amsterdam.
6. Balakrishnan, N. and Sandhu, R. A. (1996) Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive type-II censored samples. Sankhyā Ser. B, 58, 1-9.
7. Bickel, P. J. and Doksum, K. A. (1977) Mathematical Statistics. Prentice Hall, Englewood Cliffs, NJ.
8. Block, H. W. (1975) Continuous multivariate exponential extensions. In: Barlow, R. E., Fussel, J. B. and Singpurwalla, N. D. (Eds.), Reliability and Fault Tree Analysis, pp. 285-306. SIAM, Philadelphia.
9. Cohen, A. C. (1963) Progressively censored samples in life testing. Technometrics, 5, 327-329.
10. Cohen, A. C. (1995) MLEs under censoring and truncation and inference. In: Balakrishnan, N. and Basu, A. P. (Eds.), The Exponential Distribution, pp. 33-51. Gordon and Breach, Amsterdam.
11. Cramer, E. and Kamps, U. (1997) The UMVUE of P(X < Y) based on Type-II censored samples from Weinman multivariate exponential distributions. Metrika, 46, 93-121.
12. Cramer, E. and Kamps, U. (2001a) Estimation with sequential order statistics from exponential distributions. Ann. Inst. Statist. Math. (to appear).
13. Cramer, E. and Kamps, U. (2001b) Sequential k-out-of-n systems. In: Balakrishnan, N. and Rao, C. R. (Eds.), Handbook of Statistics: Advances in Reliability. Elsevier, Amsterdam (to appear).
14. David, H. A. (1981) Order Statistics. Wiley, New York, 2nd edn.
15. Engelhardt, M. (1995) Reliability estimation and applications. In: Balakrishnan, N. and Basu, A. P. (Eds.), The Exponential Distribution, pp. 71-91. Gordon and Breach, Amsterdam.
16. Epstein, B. (1957) Simple estimators or the parameters of exponential distributions when samples are censored. Ann. Inst. Statist. Math., 8, 15-26.
17. Epstein, B. and Sobel, M. (1954) Some theorems relevant to life testing from an exponential distribution. Ann. Math. Statist., 25, 373-381.
18. Johnson, N. L. and Kotz, S. (1972) Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
19. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 1. Wiley, New York, 2nd edn.
20. Joshi, P. C. (1977) Recurrence relations between moments of order statistics from exponential and truncated exponential distributions. Sankhyā Ser. B, 39, 362-371.
21. Joshi, P. C. (1979) A note on the moments of order statistics from doubly truncated exponential distribution. Ann. Inst. Statist. Math., 31, 321-324.
22. Joshi, P. C. (1982) A note on the mixed moments of order statistics from exponential and truncated exponential distributions. J. Statist. Plann. Inference, 6, 13-16.
23. Kamps, U. (1995) A Concept of Generalized Order Statistics. Teubner, Stuttgart.
24. Kamps, U. (1999) Order statistics, generalized. In: Kotz, S., Read, C. B. and Banks, D. L. (Eds.), Encyclopedia of Statistical Sciences, Update, Vol. 3, 553-557, New York, Wiley.
25. Lawless, J. F. (1982) Statistical Models and Methods for Lifetime Data. Wiley, New York.
26. Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press, London.
27. Schenk, N. (1998) Generalisierte progressiv Typ II zensierte Ordnungsstatistiken. Master's Thesis, University of Oldenburg.
28. Sen, P. K. (1986) Progressive censoring schemes. In: Kotz, S. and Johnson, N. L. (Eds.), Encyclopedia of Statistical Sciences, 7, 296-299, New York. Wiley.
29. 2-population with two degrees of freedom. Ann. Eugenics, 8, 52-56.
30. Viveros, R. and Balakrishnan, N. (1994) Interval estimation of parameters of life from progressively censored data. Technometrics, 36, 84-91.
31. Weinman, D. G. (1966) A Multivariate Extension of the Exponential Distribution. Ph.D. Thesis, Arizona State University.