Estimation and prediction based on record statistics in the presence of an outlier

References

• Ahmadi, J., and N. Balakrishnan. 2009. Pitman closeness of record values to population quantiles. Statistics & Probability Letters 79 (19):2037–44. doi:10.1016/j.spl.2009.06.016.
   Web of Science ®Google Scholar
• Ahsanullah, M. 1980. Linear prediction of record values for the two parameter exponential distribution. Annals of the Institute of Statistical Mathematics 32 (3):363–68. doi:10.1007/BF02480340.
   Web of Science ®Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1998. Records, New York: John Wiley & Sons.
   Google Scholar
• Balakrishnan, N. 1988. Recurrence relations for order statistics from n independent and non-identically distributed random variables. Annals of the Institute of Statistical Mathematics 40:273–77.
   Web of Science ®Google Scholar
• Balakrishnan, N. 1994a. On order statistics from non-identical right-truncated exponential random variables and some applications. Communications in Statistics - Theory and Methods 23 (12):3373–93. doi:10.1080/03610929408831453.
   Web of Science ®Google Scholar
• Balakrishnan, N. 1994b. On order statistics from non-identical exponential random variables and some applications (with discussion). Computational Statistics & Data Analysis 18 (2):203–53. doi:10.1016/0167-9473(94)90172-4.
   Web of Science ®Google Scholar
• Balakrishnan, N., and A. P. Basu. 1995. Exponential distribution: Theory, methods and applications. New York: Taylor & Francis.
   Google Scholar
• Balakrishnan, N., K. Davies, and J. P. Keating. 2009. Pitman closeness of order statistics to population quantiles. Communications in Statistics - Simulation and Computation 38 (4):802–20. doi:10.1080/03610910802650313.
   Web of Science ®Google Scholar
• Balakrishnan, N., U. Kamps, and M. Kateri. 2009. Minimal repair under a step-stress test. Statistics & Probability Letters 79 (13):1548–58. doi:10.1016/j.spl.2009.03.020.
   Web of Science ®Google Scholar
• Balakrishnan, N., K. F. Davies, J. P. Keating, and R. L. Mason. 2011. Pitman closeness, monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under type II censoring. Journal of Statistical Computation and Simulation 81 (8):985–99. doi:10.1080/00949651003587684.
   Web of Science ®Google Scholar
• Barnett, V., and T. Lewis. 1994. Outlier in Statistical Data, 3rd Ed. Chichester, England: John Wiley & Sons.
   Google Scholar
• Childs, A., N. Balakrishnan, and M. Moshref. 2001. On order statistics from non-identical right-truncated Lomax random variables and some applications. Statistical Papers 42 (2):187–206. doi:10.1007/s003620100050.
   Web of Science ®Google Scholar
• Cramer, E., and U. Kamps. 2001. Estimation with sequentioal order statistics from exponential distribution. Annals of the Institute of Statistical Mathematics 53 (2):307–24. doi:10.1023/A:1012470706224.
   Web of Science ®Google Scholar
• Cramer, E., and U. Kamps. 2003. Marginal distributions of sequential and generalized order statistics. Metrika 58 (3):293–310. doi:10.1007/s001840300268.
   Web of Science ®Google Scholar
• Doganaksoy, N., and N. Balakrishnan. 1997. A useful property of best linear unbiased predictors with applications to life testing. The American Statistician 51 (1):22–28. doi:10.1080/00031305.1997.10473581.
   Web of Science ®Google Scholar
• Goldberger, A. S. 1962. Best linear unbiased prediction in the generalized regression model. Journal of the American Statistical Association 57 (298):369–75. doi:10.1080/01621459.1962.10480665.
   Web of Science ®Google Scholar
• Gulati, S., and W. J. Padgett. 2003. Parametric and non-parametric inference from record-breaking data. In Lecture notes in statistics, 172. New York: Springer-Verlag,
   Google Scholar
• Kamps, U. 1995. A concept of generalized order statistics. Journal of Statistical Planning and Inference 48 (1):1–23. doi:10.1016/0378-3758(94)00147-N.
   Web of Science ®Google Scholar
• Keating, J. P., R. L. Mason, and P. K. Sen. 1993. Pitman’s measure of closeness: A comparison of statistical estimators. Philadelphia: Society for Industrial and Applied Mathematics.
   Google Scholar
• Khatib, B., and J. Ahmadi. 2014. Best linear unbiased (invariant) reconstructor for the past records from two-parameter exponential distribution. Bulletin of the Malaysian Mathematical Sciences Society 37:1017–28.
   Google Scholar
• Khatib, B., and M. Razmkhah. 2018. Estimation and prediction in the presence of an outlier under Type-II censoring. Journal of Statistical Computation and Simulation 88 (17):3251–68. doi:10.1080/00949655.2018.1509978.
   Web of Science ®Google Scholar
• Krakowski, M. 1973. The relevation transform and a generalization of the gamma distribution function. Revue Française D'automatique, Informatique, Recherche Opérationnelle. Recherche Opérationnelle 7 (V2):107–20. doi:10.1051/ro/197307V201071.
   Google Scholar
• Lau, K. S., and B. L. S. P. Rao. 1990. Characterization of the exponential distribution by the relevation transform. Journal of Applied Probability 27 (3):726–29. doi:10.2307/3214557.
   Web of Science ®Google Scholar
• Mann, N. R. 1969. Optimum estimators for linear functions of location and scale parameters. The Annals of Mathematical Statistics 40 (6):2149–55. doi:10.1214/aoms/1177697292.
   Google Scholar
• Marshall, A. W., and O. Olkin. 2007. Life distributions. New York: Springer.
   Google Scholar
• MirMostafaee, S. M. T. K., and J. Ahmadi. 2011. Point prediction of future order statistics from an exponential distribution. Statistics & Probability Letters 81 (3):360–70. doi:10.1016/j.spl.2010.11.017.
   Web of Science ®Google Scholar
• Pitman, E. J. G. 1937. The closest estimates of statistical parameters. Mathematical Proceedings of the Cambridge Philosophical Society 33 (2):212–95. doi:10.1017/S0305004100019563.
   Google Scholar
• Proschan, F. 1963. Theoretical explanation of observed decreasing failure rate. Technometrics 5 (3):375–83. doi:10.1080/00401706.1963.10490105.
   Web of Science ®Google Scholar
• Sarhan, A. E., and B. G. Greenberg. 1957. Tables for best linear estimates by order statistics of the parameters of single exponential distributions from singly and doubly censored samples. Journal of the American Statistical Association 52 (277):58–87. doi:10.1080/01621459.1957.10501369.
   Web of Science ®Google Scholar