International Journal of Reliability and Applications

The Korean Reliability Society (한국신뢰성학회)
권호 표지

Computational procedures for exponential life model incorporating Bayes and shrinkage techniques

  • Al-Hemyari, Zuhair A. (Ministry of Higher Education) ;
  • Al-Dabag, H.A. (Babil University) ;
  • Al-Humairi, Ali Z. (University of Duisburg-Essen)
  • Received : 2015.01.20
  • Accepted : 2015.10.13
  • Published : 2015.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

It is well known that using any additional information in the estimation of unknown parameters with new sample of observations diminishes the sampling units needed and minimizes the risk of new estimators. There are many rational reasons to assure that the existence of additional information in practice and there exists many practical cases in which additional information is available in the form of target value (initial value) about the unknown parameters. This article is described the problem of how the prior initial value about the unknown parameters can be utilized and combined with classical Bayes estimator to get a new combination of Bayes estimator and prior value to improve the properties of the new combination. In this article, two classes of Bayes-shrinkage and preliminary test Bayes-shrinkage estimators are proposed for the scale parameter of exponential distribution. The bias, risk and risk ratio expressions are derived and studied. The performance of the proposed classes of estimators is studied for different choices of constants engaged in the estimators. The comparisons, conclusions and recommendations are demonstrated.

Keywords

References

  1. Al-Hemyari, Z. A. and Al-Dolimi, J. (2014). Optimized shrinkage estimators of reliability function in a failure-time model with prior information and time censored data. Journal of Risk and Reliability, 228, 578-589.
  2. Al-Hemyari, Z. A. and Al-Dabag, H. A. (2014). Two classes of Bayes-shrinkage estimators for Weibull lifetime model. Accepted for publication in International Journal of Data Analysis Techniques and Strategies.
  3. Al-Hemyari, Z. A. and Al-Ali, A. R. (2013). Optimized estimation technique of Weibull lifetime model by using prior information, International Journal of Reliability and Safety, 7, 276-292. https://doi.org/10.1504/IJRS.2013.057094
  4. Al-Hemyari, Z. A., Al-Saidy O. M. and Al-Ali, A. R. (2013). On simple estimation technique for the reliability function of exponential failure model, International Journal of Reliability and Applications, 14, 79-96.
  5. Al-Hemyari, Z. A. and Jehel, A. K. (2011). Pooling shrinkage estimator of Reliability for Exponential Failure Model using the sampling plan (n, C, T), International Journal of Reliability and Applications. 12, 61-77.
  6. Al-Hemyari, Z. A. (2010). Some estimators for the scale parameter and reliability function of Weibull lifetime data, Journal of Risk and Reliability, 224, 197-205.
  7. Bain, L. J. and Engelhardt, M. (1991). Statistical analysis of reliability and life testing models, New York, NY: Marcel Dekker.
  8. Bennett, G., Kemble, and Martz, H. F. (2006). An empirical Bayes estimator for the scale parameter of the two parameter Weibull distribution, Naval Research Logistics Quarterly, 20, 387-393.
  9. Bernardo, J. M., Smith, A. F. M. (2000). Bayesian theory, John Wiley & Sons Ltd. West Sussex: England.
  10. Chiou, P. (1993). Empirical Bayes shrinkage estimation of reliability in the exponential Distribution, Communications in Statistics-Theory and Methods, 22, 1483-1494. https://doi.org/10.1080/03610929308831098
  11. Chiou, P. (1992). Shrinkage estimation of reliability in the exponential distribution. Communications in Statistics-Theory and Methods, 21, 1745-1758. https://doi.org/10.1080/03610929208830876
  12. Chiou, P. (1992). Shrinkage estimation of reliability in the exponential distribution. Communications in Statistics-Theory and Methods, 21, 1745-1758. https://doi.org/10.1080/03610929208830876
  13. Chiou, P. (1990). Estimation of scale parameters for two exponential distributions, IEEE Transaction on Reliability, 39, 106-109. https://doi.org/10.1109/24.52620
  14. Chiou, P. (1987). A Preliminary test estimator of reliability in a life-testing model, IEEE Transaction on Reliability, 36, 408-410.
  15. Davis, D. J. (1952). The analysis of some failure data, Journal of American Statistical Association, 47, 113-150. https://doi.org/10.1080/01621459.1952.10501160
  16. Davison, A. C. (2003). Statistical models, Cambridge University Press: UK
  17. Huntsberger, D. V. (1955). A generalization of a preliminary testing procedure for pooling data. Ann. Math. Statist., 26, 734-743. https://doi.org/10.1214/aoms/1177728431
  18. Kambo, N. S., Handa, B. R. and Al-Hemyari, Z. A. (1992). On Huntsberger type shrinkage estimator. Communications in Statistics-Theory and Methods, l2, 823-841.
  19. Kambo, N. S., Handa, B. R. and Al-Hemyari, Z. A. (1990). On shrunken estimators for exponential scale parameter, Journal of Statistical Planning and Inferences, 24, 87-94. https://doi.org/10.1016/0378-3758(90)90019-Q
  20. Katti, S. K. (1962). Use of some a prior knowledge in the estimation of means from double samples, Biometrics, 18, 139-147. https://doi.org/10.2307/2527452
  21. Kourouklis, S. (1994). Estimation of 2-parameter exponential distribution with prior Information, IEEE Transaction on Reliability, 43, 446-450. https://doi.org/10.1109/24.326444
  22. Lanping, Li. (2011). Bayesian shrinkage estimation in exponential distribution based on record values, International Conference on Computational and Information Sciences, Chengdu, Sichuan Chengdu, 1159-1162.
  23. Lemmer, H. (1981). From ordinary to Baysian shrinkage estimators, South Africa Statist. Journal, 15, 57-72.
  24. Lemmer, H. (2006). Shrinkage Estimators, In: Encyclopedia of Statistical Sciences, Second Edition, 12, 7704-7707 (Eds. S. Kotz, N. Balakrishnan, C. B. Read and B. Vidakovic), New York: John Wiley.
  25. Mann, N. R., Schafer, R. E and Singpurwalla, N. D. (1974). Methods of statistical analysis of reliability and life data, Wiley: New York.
  26. Mehta, J. S. and Srinivasan, R. (1971). Estimation of the mean by shrinkage to a Point, Journal of American Statistical Association, 66, 86-90. https://doi.org/10.1080/01621459.1971.10482224
  27. Pandey, M. and Singh, V. P. (1989). Bayesian shrinkage estimation of reliability from a censored sample from a finite range failure time model, Microelectronics and Reliability, 29, 955-958. https://doi.org/10.1016/0026-2714(89)90019-X
  28. Pandey, M. (1988). Bayesian approach to shrinkage estimation of the scale parameter of Weibull distribution, South Africa Statist. Journal, 22, 1-13.
  29. Pandey, M. and Upadhyay, S. K. (1987). Bayesian shrinkage estimation reliability with Weibull distribution of components, Microelectronics Reliability, 27, 625-628. https://doi.org/10.1016/0026-2714(87)90005-9
  30. Pandey, M. and Upadhyay, S. K. (1985a). Bayesian shrinkage estimator of Weibull Parameters, IEEE Transaction in Reliability, 34, 491-494.
  31. Pandey, M. and Upadhyay, S. K. (1985b). Bayesian shrinkage estimation of reliability in parallel system with exponential failure of the components, Microelectronics Reliability, 25, 899-903. https://doi.org/10.1016/S0026-2714(85)80017-2
  32. Pandey, M. and Upadhyay, S. K. (1985c). Bayesian shrinkage estimation of reliability from censored sample with exponential failure model, South Africa Statist. Journal, 19, 21-33.
  33. Pandey, M. (1983). Shrunken estimators of the of Weibull shape parameters in censored samples, IEEE Transaction in Reliability, 32, 200-203.
  34. Parkash, G. and Singh, D. C. (2009). A Bayesian shrinkage approach in Weibull type-II censored data using prior point information, REVSTAT-Statistical Journal, 7, 171-187.
  35. Sarhan, A. E. and Greenberg, B. G. (1962) Contribution to Order Statistics, Wiley: New York.
  36. Shanubhogue, A. and Jiheel, A. K. (2013). Bayes pretest estimation of scale parameter of Weibull distribution under different loss functions using progressive type II censored sample, Journal of Reliability and Statistical Studies, 6, 101-113.
  37. Sinha, S. K. (1986). Reliability and Life Testing, Wiley Eastern Limited: New Delhi.
  38. Soland, R. M. (1968). Bayesian analyses of the Weibull process with unknown scale parameter and its application to acceptance sampling, IEEE Transactions on Reliability, 17, 84-90.
  39. Thompson, J. R. (1968). Some shrinkage techniques for estimating the mean, Journal of American Statistical Association, 63, 113-123.
  40. Upadhyay, S. K. and Singh, U. (1992). Bayes estimators in presence of a guess Value, Communications in Statistics-Simulation, 21, 1181-1198. https://doi.org/10.1080/03610919208813072
  41. Yang, L., Zhou, H. and Yuan, S. (2013). Bayes estimation of parameters of exponential distribution under a bounded loss function, Research Journal of Mathematic and Statistics, 5, 28-31.
  42. Zhao, Y., Lee, A. H. and Barnes, T. (2010). On application of the empirical Bayes Shrinkage in epidemiological settings, International Journal of Environmental Research and Public Health, 7, 380-394. https://doi.org/10.3390/ijerph7020380