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Estimation and testing procedures for the reliability functions of a family of lifetime distributions based on records

Author

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  • Ajit Chaturvedi

    (University of Delhi)

  • Ananya Malhotra

    (University of Delhi)

Abstract

A family of lifetime distributions is considered. Two measures of reliability are considered, R(t) = P(X > t) and P = P(X > Y). Point estimation and testing procedures are developed for R(t) and P based on records. Two types of point estimators are developed—uniformly minimum variance unbiased estimators and maximum likelihood estimators. A comparative study of different methods of estimation is done through simulation studies. Testing procedures are developed for the hypothesis related to different parametric functions.

Suggested Citation

  • Ajit Chaturvedi & Ananya Malhotra, 2017. "Estimation and testing procedures for the reliability functions of a family of lifetime distributions based on records," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 836-848, November.
  • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-016-0531-2
    DOI: 10.1007/s13198-016-0531-2
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    References listed on IDEAS

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    1. M. Arashi & M. Emadi, 2008. "Evidential inference based on record data and inter-record times," Statistical Papers, Springer, vol. 49(2), pages 291-301, April.
    2. T. C. T. Kotiah, 1975. "Letter to the Editor—Errata," Operations Research, INFORMS, vol. 23(5), pages 1043-1044, October.
    3. Ajit Chaturvedi & Uma Rani, 1997. "Estimation procedures for a family of density functions representing various life-testing models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 213-219, January.
    4. Ajit Chaturvedi & Khumukcham Gopichandra Singh, 2006. "Bayesian estimation procedures for a family of lifetime distributions under squared-error and entropy losses," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 179-198.
    5. R. Arabi Belaghi & M. Arashi & S. M. M. Tabatabaey, 2015. "On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 1-23, January.
    6. Edward L. Pugh, 1963. "The Best Estimate of Reliability in the Exponential Case," Operations Research, INFORMS, vol. 11(1), pages 57-61, February.
    7. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    8. M. Mahmoud & H. Al-Nagar, 2009. "On generalized order statistics from linear exponential distribution and its characterization," Statistical Papers, Springer, vol. 50(2), pages 407-418, March.
    9. M. Razmkhah & H. Morabbi & J. Ahmadi, 2012. "Comparing two sampling schemes based on entropy of record statistics," Statistical Papers, Springer, vol. 53(1), pages 95-106, February.
    10. Ajit Chaturvedi & Sanjeev Tomer, 2003. "UMVU estimation of the reliability function of the generalized life distributions," Statistical Papers, Springer, vol. 44(3), pages 301-313, July.
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