Communications for Statistical Applications and Methods

  • 제25권4호
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  • Pages.355-371
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  • 2018
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Maximum penalized likelihood estimation for a stress-strength reliability model using complete and incomplete data

  • 투고 : 2018.02.13
  • 심사 : 2018.05.09
  • 발행 : 2018.07.31
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초록

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

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참고문헌

  1. Ali MM, Pal M, and Woo J (2012). Estimation of P(Y < X) in a four-parameter generalized gamma distribution, Austrian Journal of Statistics, 41, 197-210.
  2. Al-Mutairi DK, Ghitany ME, and Kundu D (2013). Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics Theory and Methods, 42, 1443-1463. https://doi.org/10.1080/03610926.2011.563011
  3. Asgharzadeh A, Valiollahi R, and Raqab M (2011). Stress-strength reliability of Weibull distribution based on progressively censored samples, SORT, 35, 103-124.
  4. Badar MG and Priest AM (1982). Statistical aspects of fiber and bundle strength in hybrid composites. In T. Hayashi, K. Kawata, and S. Umekawa (Eds.), Progress in Science and Engineering Composites (pp. 1129-1136), ICCM-IV, Tokyo.
  5. Balakrishnan N and Aggarwala R (2000). Progressive Censoring: Theory, Methods and Applications, Birkhauser, Boston.
  6. Basu AP (1964). Estimates of reliability for some distributions useful in reliability, Technometrics, 6, 215-219. https://doi.org/10.1080/00401706.1964.10490165
  7. Beg MA (1980). On the estimation of P(Y < X) for two-parameter exponential distribution, Metrika, 27, 29-34. https://doi.org/10.1007/BF01893574
  8. Birnbaum ZW (1956). On a use of the Mann-Whitney statistic. In Proceedings of Third Berkeley Symposium on Mathematical Statistics and Probability, (Vol. 1, pp. 13-17), University of California Press, CA.
  9. Chen MH and Shao QM (1999). Monte Carlo estimation of Bayesian credible and HPD intervals, Journal of Computational and Graphical Statistics, 8, 69-92.
  10. Downtown F (1973). The estimation of P(Y < X) in the normal case, Technometrics, 15, 551-558.
  11. Enis P and Geisser S (1971). Estimation of the probability that P(Y < X), Journal of the American Statistical Association, 66, 162-168.
  12. Ghitany ME, Al-Mutairi DK, and Aboukhamseen SM (2015). Estimation of the reliability of a stressstrength system from power Lindley distributions, Communications in Statistics Simulation and Computation, 44, 118-136. https://doi.org/10.1080/03610918.2013.767910
  13. Greco L and Ventura L (2011). Robust inference for the stress-strength reliability, Statistical Papers, 52, 773-788. https://doi.org/10.1007/s00362-009-0286-9
  14. Hussian MA (2013). On estimation of stress-strength model for generalized inverted exponential distribution, Journal of Reliability and Statistical Studies, 6, 55-63.
  15. Iwase K (1987). On UMVU estimators of P(Y < X) in the 2-parameter exponential case, Memoirs of the Faculty of Engineering, Hiroshima University, 9, 21-24.
  16. Kelley GD, Kelley JA, and Schucany WR (1976). Efficient estimation of P(Y < X) in the exponential case, Technometrics, 18, 359-360.
  17. Kundu D and Gupta RD (2006). Estimation of p(Y < X) for Weibull distribution, IEEE Transactions on Reliability, 55, 270-280. https://doi.org/10.1109/TR.2006.874918
  18. Kundu D and Raqab MZ (2009). Estimation of R = P(Y < X) for three-parameter Weibull distribution, Statistics and Probability Letters, 79, 1839-1846. https://doi.org/10.1016/j.spl.2009.05.026
  19. Krishnamoorthy K, Mukherjee S, and Guo H (2007). Inference on reliability in two-parameter exponential stress-strength model, Metrika, 6, 261-273.
  20. Lindley DV (1980). Approximation Bayesian methods, Trabajos de Estadistica, 21, 223-237.
  21. McCool JI (1991). Inference on P(X < Y) In the Weibull case, Communications in Statistics Simulation and Computation, 20, 129-148. https://doi.org/10.1080/03610919108812944
  22. Najarzadegan H, Babaii S, Rezaei S, and Nadarajah S (2016). Estimation of P(Y < X) for the Levy distribution, Hacettepe Journal of Mathematics and Statistics, 45, 957-972.
  23. Pal M, Ali MM, and Woo J (2005). Estimation and testing of P(Y > X) in two-parameter exponential distributions, Statistics, 39, 415-428. https://doi.org/10.1080/02331880500274031
  24. Raqab MZ and Kundu D (2005). Comparison of different estimators of P(Y < X) for a scaled Burr Type X distribution, Communications in Statistics Simulation and Computation, 34, 465-483. https://doi.org/10.1081/SAC-200055741
  25. Rezaei S, Tahmasbi R, and Mahmoodi M (2010). Estimation of P[Y < X] for generalized Pareto distribution, Journal of Statistical Planning and Inference, 140, 480-494. https://doi.org/10.1016/j.jspi.2009.07.024
  26. Saracoglu B, Kinaci I, and Kundu D (2012). On estimation of R = p(Y < X) for exponential distribution under progressive type-II censoring, Journal of Statistical Computation and Simulation, 82, 729-744. https://doi.org/10.1080/00949655.2010.551772
  27. Sathe YS and Shah SP (1981). On estimation P(Y < X) for the exponential distribution, Communications in Statistics and Theory and Methods, 10, 39-47. https://doi.org/10.1080/03610928108828018
  28. Shahsanaei F and Daneshkhah A (2013). Estimation of stress-strength model in generalized linear failure rate distribution, ArXiv:1312:0401v1.
  29. Tong H (1974). A note on the estimation of P(Y < X) in the exponential case, Technometrics, 16, 625.
  30. Tong H (1977). On the estimation of P(Y < X) for exponential families, IEEE Transactions on Reliability, 26, 54-56.
  31. Wong A (2012). Interval estimation of P(Y < X) for generalized Pareto distribution, Journal of Statistical Planning and Inference, 142, 601-607. https://doi.org/10.1016/j.jspi.2011.04.024
  32. Zheng M (2013). Penalized Maximum Likelihood Estimation of Two-Parameter Exponential Distributions. A Project submitted to the faculty of graduate school of the University of Minnesota.