Advertisement

Statistical Papers

, 33:203 | Cite as

Estimation for one- and two-parameter exponential distributions under multiple type-II censoring

  • K. Balasubramanian
  • N. Balakrishnan
Articles

Abstract

In this paper, we derive explicit best linear unbiased estimators for one- and two-parameter exponential distributions when the available sample is multiply Type-II censored. Further, after noting that the maximum likelihood estimators do not exist explicitly, we propose some linear estimators by approximating the likelihood equations appropriately. Some illustrative examples from life-testing experiments are also presented.

Keywords

Exponential Distribution Maximum Likelihood Estimator Linear Estimator Likelihood Equation Good Linear Unbiased Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bain, L. J. (1978).Statistical Analysis of Reliability and Life-Testing Models-Theory and Practice, Marcel Dekker, New York.Google Scholar
  2. Balakrishnan, N. (1990). On the maximum likelihood estimation of the location and scale parameters of exponential distribution based on multiply Type II censored samples,J. Appl. Statist. 17, 55–61.CrossRefGoogle Scholar
  3. Balakrishnan, N. and Cohen, A. C. (1990).Order Statistics and Inference: Estimation Methods, Academic Press, Boston.Google Scholar
  4. David, H. A. (1981).Order Statistics, Second edition, John Wiley & Sons, New York.MATHGoogle Scholar
  5. Epstein, B. (1956). Simple estimators of the parameters of exponential distributions when samples are censored,Ann. Inst. Statist. Math. 8, 15–26.MATHMathSciNetCrossRefGoogle Scholar
  6. Epstein, B. (1962). Simple estimates of the parameters of exponential distributions, In:Contributions to Order Statistics (Eds., A. E. Sarhan and B. G. Greenberg), p. 361–371, John Wiley & Sons, New York.Google Scholar
  7. Epstein, B. and Sobel, M. (1953). Life testing,J. Amer. Statist. Assoc. 48, 486–502.MATHCrossRefMathSciNetGoogle Scholar
  8. Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testing from an exponential distribution,Ann. Math. Statist. 25, 373–381.CrossRefMathSciNetMATHGoogle Scholar
  9. Herd, R. G. (1956). Estimation of the parameters of a population from a multicensored sample,Ph.D. Thesis, Iowa State College, Ames, Iowa.Google Scholar
  10. Kambo, N. S. (1978). Maximum likelihood estimators of the location and scale parameters of the exponential distribution from a censored sample,Commun. Statist.-Theor. Meth.A7(12), 1129–1132.CrossRefMathSciNetGoogle Scholar
  11. Lawless, J. F. (1982).Statistical Models & Methods For Lifetime Data, John Wiley & Sons, New York.MATHGoogle Scholar
  12. Mann, N. R., Schafer, R. E., and Singpurwalla, N. D. (1974).Methods for Statistical Analysis of Reliability and Life Data, John Wiley & Sons, New York.MATHGoogle Scholar
  13. Sarhan, A. E. and Greenberg, B. G. (1957). Tables for best linear estimates by order statistics of the parameters of single exponential distributions from singly and doubly censored samples,J. Amer. Statist. Assoc. 52, 58–87.MATHCrossRefMathSciNetGoogle Scholar
  14. Sarhan, A. E. and Greenberg, B. G. (1958). Estimation problems in exponential distribution using order statistics, InProc. of the Statistical Techniques in Missile Evaluation Symposium, Virginia, p. 123–173.Google Scholar
  15. Sarhan, A. E. and Greenberg, B. G. (Eds.) (1962).Contributions to Order Statistics, John Wiley & Sons, New York.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • K. Balasubramanian
    • 1
  • N. Balakrishnan
    • 2
  1. 1.Indian Statistical InstituteNew DelhiIndia
  2. 2.McMaster UniversityHamiltonCanada

Personalised recommendations