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IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA

Year 2014, Volume: 7 Issue: 3, 71 - 79, 01.09.2014

Abstract

This study presents two different kinds of preliminary test estimators based on Type II censoredobservations in the two parameters exponential model. We deŞne MLE and MRE preliminary test estimatorsin the same fashion as in the ordinary preliminary test estimator using relevant combinations of MLE andMRE estimators. Exact bias and MSE expressions for the proposed estimators are derived . We compare theMSEs and obtain some intervals for the parameter of interest in which the preliminary test type estimatorsoutperforms the MLE and MRE estimators. Some graphical representations are given for the illustrationpurpose. Finally, we conclude this approach by a useful discussion for practical purposes and a summary

References

  • Arabi Belaghi, R. , Arashi, M. , Tabatabaey, S. M. M (2015). On the construction of preliminary test estimator based on record values for Burr XII model, Communication in Statistics - Theory and Methods, 44, 1-23.
  • Baklizi, A. (2005). Preliminary test estimation in the two parameter exponential distribution with time censored data, Applied Mathematics and Computation , 163, 639-643.
  • Balakrishnan, N. (1990). On the Maximum likelihood estimation of the location and scale parameter of exponential distribution based on multiply Type II censored samples, Journal of Journal of Applied Statistics, 17(1), 55-61.
  • Balakrishnan, N., Basu, A.P. (Eds.) (1995). The Exponential Distribution: Theory, Methods and Appli- cations. Gordon and Breach, Newark, NJ.
  • Bancroft, T. A. (1944). On biases in estimation due to use of preliminary tests of signiŞcance, Ann. Math. , 15, 190-204.
  • Johnson, N. L., Kotz, S. , Balakrisnnan, N. (1982). Continuous univariate distribution, vol 1, Wiley, New York.
  • Kibria, B. M. G. (2004). Performance of the shrinkage preliminary tests ridge regression estimators based on the conflicting of W, LR and LM tests, Journal of Statistical Computation and Simulation, 74(11), 793-810.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2010). Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples. Statistical Papers, 51, 757-773.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2006). Optimum critical value for pre-test estimators. Communication in Statistics - Theory and Methods , 35(2), 309-320.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2005). Comparison between Han-Bancroft and Brook method to determine the optimum signiŞcance level for pre-test estimator. J. prob. Stat. Sci., 3, 293-303. [11] Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2004). Preliminary test ridge regression estimators with Student’s t errors and conflicting test-statistics, Metrika, 59(2), 105-124.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (1993). Performance of shrinkage preliminary test estimator in regression analysis, Jahangrinagar Rev., A17, 133-148.
  • Lawless, J. F., (1982). Statistical Models and Models for Lifetime Data Analysis, Wiley, New York.
  • Mann, N., R., Schafer, R., E., Singpurwalla, N., D., (1974). Methods for Statistical Analysis of Reliability and Life Data, New York, John Wiley and Sons.
  • Saleh, A. K. Md. Ehsanes (2006). Theory of preliminary test and stein-type estimations with applications, John Wiley, New York.
  • Saleh, A. K. Md. Ehsanes and Kibria, B. M. G. (1993). Performance of some new preliminary test ridge regression estimators and their properties, Communication in Statistics - Theory and Methods, 22(10), 2747-2764.
Year 2014, Volume: 7 Issue: 3, 71 - 79, 01.09.2014

Abstract

References

  • Arabi Belaghi, R. , Arashi, M. , Tabatabaey, S. M. M (2015). On the construction of preliminary test estimator based on record values for Burr XII model, Communication in Statistics - Theory and Methods, 44, 1-23.
  • Baklizi, A. (2005). Preliminary test estimation in the two parameter exponential distribution with time censored data, Applied Mathematics and Computation , 163, 639-643.
  • Balakrishnan, N. (1990). On the Maximum likelihood estimation of the location and scale parameter of exponential distribution based on multiply Type II censored samples, Journal of Journal of Applied Statistics, 17(1), 55-61.
  • Balakrishnan, N., Basu, A.P. (Eds.) (1995). The Exponential Distribution: Theory, Methods and Appli- cations. Gordon and Breach, Newark, NJ.
  • Bancroft, T. A. (1944). On biases in estimation due to use of preliminary tests of signiŞcance, Ann. Math. , 15, 190-204.
  • Johnson, N. L., Kotz, S. , Balakrisnnan, N. (1982). Continuous univariate distribution, vol 1, Wiley, New York.
  • Kibria, B. M. G. (2004). Performance of the shrinkage preliminary tests ridge regression estimators based on the conflicting of W, LR and LM tests, Journal of Statistical Computation and Simulation, 74(11), 793-810.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2010). Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples. Statistical Papers, 51, 757-773.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2006). Optimum critical value for pre-test estimators. Communication in Statistics - Theory and Methods , 35(2), 309-320.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2005). Comparison between Han-Bancroft and Brook method to determine the optimum signiŞcance level for pre-test estimator. J. prob. Stat. Sci., 3, 293-303. [11] Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (2004). Preliminary test ridge regression estimators with Student’s t errors and conflicting test-statistics, Metrika, 59(2), 105-124.
  • Kibria, B. M. G. and Saleh, A. K. Md. Ehsanes (1993). Performance of shrinkage preliminary test estimator in regression analysis, Jahangrinagar Rev., A17, 133-148.
  • Lawless, J. F., (1982). Statistical Models and Models for Lifetime Data Analysis, Wiley, New York.
  • Mann, N., R., Schafer, R., E., Singpurwalla, N., D., (1974). Methods for Statistical Analysis of Reliability and Life Data, New York, John Wiley and Sons.
  • Saleh, A. K. Md. Ehsanes (2006). Theory of preliminary test and stein-type estimations with applications, John Wiley, New York.
  • Saleh, A. K. Md. Ehsanes and Kibria, B. M. G. (1993). Performance of some new preliminary test ridge regression estimators and their properties, Communication in Statistics - Theory and Methods, 22(10), 2747-2764.
There are 15 citations in total.

Details

Other ID JA76CA36AF
Journal Section Research Article
Authors

R. Arabi Belaghi This is me

Özlem Gürünlü Alma This is me

Minoo Aminnejad. This is me

Publication Date September 1, 2014
Published in Issue Year 2014 Volume: 7 Issue: 3

Cite

APA Belaghi, R. A., Alma, Ö. G., & Aminnejad., M. (2014). IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA. Istatistik Journal of The Turkish Statistical Association, 7(3), 71-79.
AMA Belaghi RA, Alma ÖG, Aminnejad. M. IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA. IJTSA. September 2014;7(3):71-79.
Chicago Belaghi, R. Arabi, Özlem Gürünlü Alma, and Minoo Aminnejad. “IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA”. Istatistik Journal of The Turkish Statistical Association 7, no. 3 (September 2014): 71-79.
EndNote Belaghi RA, Alma ÖG, Aminnejad. M (September 1, 2014) IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA. Istatistik Journal of The Turkish Statistical Association 7 3 71–79.
IEEE R. A. Belaghi, Ö. G. Alma, and M. Aminnejad., “IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA”, IJTSA, vol. 7, no. 3, pp. 71–79, 2014.
ISNAD Belaghi, R. Arabi et al. “IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA”. Istatistik Journal of The Turkish Statistical Association 7/3 (September 2014), 71-79.
JAMA Belaghi RA, Alma ÖG, Aminnejad. M. IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA. IJTSA. 2014;7:71–79.
MLA Belaghi, R. Arabi et al. “IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA”. Istatistik Journal of The Turkish Statistical Association, vol. 7, no. 3, 2014, pp. 71-79.
Vancouver Belaghi RA, Alma ÖG, Aminnejad. M. IMPROVED ESTIMATORS OF THE EXPONENTIAL MODEL BASED ON TYPE TWO CENSORED DATA. IJTSA. 2014;7(3):71-9.