Advertisement

Statistical inferences based on INID progressively type II censored order statistics

  • M. Razmkhah
  • S. Simriz
Article
  • 99 Downloads

Abstract

Suppose that the failure times of the units placed on a life-testing experiment are independent but nonidentically distributed random variables. Under progressively type II censoring scheme, distributional properties of the proposed random variables are presented and some inferences are made. Assuming that the random variables come from a proportional hazard rate model, the formulas are simplified and also the amount of Fisher information about the common parameters of this family is calculated. The results are also extended to a fixed covariates model. The performance of the proposed procedure is investigated via a real data set. Some numerical computations are also presented to study the effect of the proportionality rates in view of the Fisher information criterion. Finally, some concluding remarks are stated.

Keywords

Fisher information Maximum likelihood estimator Cramer–Rao lower bound Proportional hazard rate family Exponential family Weibull distribution Fixed covariates model 

Notes

Acknowledgements

The authors would like to thank an anonymous referee and the associate editor for their useful comments and constructive criticisms on the original version of this manuscript which led to this considerably improved version. This research was supported by a Grant from Ferdowsi University of Mashhad (MS90212RZM).

References

  1. Abo-Eleneen, Z. A. (2008). Fisher information in type II progressive censored samples. Communications in Statistics-Theory and Methods, 37, 682–691.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Balakrishnan, N. (2007). Progressive censoring methodology: an appraisal. Test, 16, 211–259.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Balakrishnan, N., Aggarwala, R. (2000). Progressive censoring: Theory, methods and applications. Boston: Birkhauser.Google Scholar
  4. Balakrishnan, N., Burkschat, M., Cramer, E., Hofmann, G. (2008). Fisher information based progressive censoring plans. Computational Statistics and Data Analysis, 53, 366–380.Google Scholar
  5. Balakrishnan, N., Cramer, E. (2008). Progressive censoring from heterogeneous distributions with applications to robustness. Annals of the Institute of Statistical Mathematics, 60, 151–171.Google Scholar
  6. Balakrishnan, N., Cramer, E. (2014). The art of progressive censoring: applications to reliability and quality. New York: Birkhauser.Google Scholar
  7. Balakrishnan, N., Cramer, E., Kamps, U., Schenk, N. (2001). Progressive type II censored order statistics from exponential distributions. Statistics, 35, 537–556.Google Scholar
  8. Burkschat, M., Cramer, E., Kamps, U. (2006). On optimal schemes in progressive censoring. Statistics & Probability Letters, 76, 1032–1036.Google Scholar
  9. Cramer, E., Lenz, U. (2010). Association of progressively type II censored order statistics. Journal of Statistical Planning and Inference, 140, 576–583.Google Scholar
  10. Fischer, T., Balakrishnan, N., Cramer, E. (2008). Mixture representation for order statistics from INID progressively censoring and its applications. Journal of Multivariate Analysis, 99, 1999–2015.Google Scholar
  11. Lawless, J. L. (2003). Statistical models and methods for lifetime data (2nd ed.). New York: Wiley.Google Scholar
  12. Lehmann, E. L., Casella, G. (1998). Theory of point estimation (2nd ed.). New York: Springer.Google Scholar
  13. Mao, T., Hu, T. (2010). Stochastic properties of INID progressive type II censored order statistics. Journal of Multivariate Analysis, 101, 1493–1500.Google Scholar
  14. Proschan, F. (1963). Theoretical explanation of observed decreasing failure rate. Technometrics, 5, 375–383.Google Scholar
  15. Razmkhah, M., Ahmadi, J., Khatib, B. (2008). Nonparametric confidence intervals and tolerance limits based on minima and maxima. Communications in Statistics-Theory and Methods, 37, 1525–1542.Google Scholar
  16. Rezapour, M., Alamatsaz, M. H., Balakrishnan, N., Cramer, E. (2013). On properties of progressively Type II censored order statistics arising from dependent and non-identical random variables. Statistical Methodology, 10, 58–71.Google Scholar
  17. Zheng, G., Park, S. (2004). On the Fisher information in multiply censored and progressively censored data. Communications in Statistics-Theory and Methods, 23, 1821–1835.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

Personalised recommendations