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Original Articles

Estimation of the system reliability for generalized inverse Lindley distribution based on different sampling designs

, &
Pages 1532-1546 | Received 15 Nov 2018, Accepted 09 Dec 2019, Published online: 11 Jan 2020

References

  • Akgül, F. G., Ş. Acıtaş, and B. Şenoğlu. 2018. Inference on stress-strength reliability based on ranked set sampling data in case of Lindley distribution. Journal of Statistical Computation and Simulation 88 (15):3018–32. doi:10.1080/00949655.2018.1498095.
  • Akgül, F. G., and B. Şenoğlu. 2017. Estimation of P(X<Y) using ranked set sampling for the Weibull distribution. QTQM 14 (3):296–309.
  • Al-Mutairi, D. K., M. E. Ghitany, and D. Kundu. 2013. Inferences on stress-strength reliability from Lindley distribution. Communications in Statistics - Theory and Methods 42 (8):1443–63. doi:10.1080/03610926.2011.563011.
  • Al-Nasser, A. D. 2007. L ranked set sampling: A generalized procedure for robust visual sampling. Communications in Statistics - Simulation and Computation 36 (1):33–43. doi:10.1080/03610910601096510.
  • Al-Saleh, M. F., and S. A. Al-Hadrami. 2003. Parametric estimation for the location parameter for symmetric distributions using moving extremes ranked set sampling with application to trees data. Environmetrics 14 (7):651–64. doi:10.1002/env.610.
  • Asgharzadeh, A., S. Nadarajah, and F. Sharafi. 2017. Generalized inverse Lindley distribution with application to Danish fire insurance data. Communications in Statistics - Theory and Methods 46 (10):5001–21. doi:10.1080/03610926.2015.1096394.
  • Birnbaum, Z. M. 1956. On a use of the Mann-Whitney statistics. Proc. Third Berkeley Symp. Math. Statist. Probab. Contributions to the Theory of Statistics and Probability, Vol. 1, Univ. of California Press, Berkeley, 13–17.
  • Chen, Z., Z. D. Bai, and B. K. Sinha. 2004. Ranked set sampling: Theory and applications. New York, NY, USA: Springer.
  • Dell, T. R., and J. L. Clutter. 1972. Ranked set sampling theory with order statistics background. Biometrics 28 (2):545–53. doi:10.2307/2556166.
  • Downton, F. 1973. On the estimation of Pr(Y<X) in the normal case. Technometrics 15:551–8.
  • Ghitany, M. E., D. K. Al-Mutairi, and S. M. Aboukhamseen. 2015. Estimation of the reliability of a stress-strength system from power Lindley distributions. Communications in Statistics - Simulation and Computation 44 (1):118–36. doi:10.1080/03610918.2013.767910.
  • Ghitany, M. E., D. K. Al-Mutairi, N. Balakrishnan, and L. J. Al-Enezi. 2013. Power Lindley distribution and associated inference. Computational Statistics & Data Analysis 64:20–33. doi:10.1016/j.csda.2013.02.026.
  • Ghitany, M. E., F. Alqallaf, D. K. Al-Mutairi, and H. A. Husain. 2011. A two-parameter weighted Lindley distribution and its applications to survival data. Mathematical and Computers Simulation 81 (6):1190–201. doi:10.1016/j.matcom.2010.11.005.
  • Hossain, S. S., and H. A. Muttlak. 2006. Hypothesis tests on the scale parameter using median ranked set sampling. Statistica 66 (4):415–33.
  • Kundu, D., and R. D. Gupta. 2006. Estimation of (Y<X) for Weibull distributions. IEEE Transactions on Reliability 55:270–80. doi:10.1109/TR.2006.874918.
  • Lindley, D. V. 1958. Fiducial distributions and Bayes theorem. Journal of the Royal Statistical Society: Series B (Methodological) 20:102–7. doi:10.1111/j.2517-6161.1958.tb00278.x.
  • Mahdizadeh, M., and E. Zamanzade. 2018. A new reliability measure in ranked set sampling. Statistical Papers 59 (3):861–91. doi:10.1007/s00362-016-0794-3.
  • McIntyre, G. A. 1952. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3 (4):385–90. doi:10.1071/AR9520385.
  • Muttlak, H. A. 1997. Median ranked set sampling. Journal of Applied Statistical Science 6 (4):245255.
  • Muttlak, H. A. 2003. Modified ranked set sampling methods. Pakistan Journal of Statistics 19 (3):315–23.
  • Muttlak, H. A., and W. A. Abu-Dayyeh. 2004. Weighted modified ranked set sampling methods. Applied Mathematics and Computation 151 (3):645–57. doi:10.1016/S0096-3003(03)00367-9.
  • Muttlak, H. A., W. A. Abu-Dayyeh, M. F. Saleh, and E. Al-Sawi. 2010. Estimating P(Y < X) using ranked set sampling in case of the exponential distribution. Communications in Statistics Theory Methods 39:1855–68.
  • Nadarajah, S., H. S. Bakouch, and R. Tahmasbi. 2011. A generalized Lindley distribution. Sankhya B 73 (2):331–59. doi:10.1007/s13571-011-0025-9.
  • Patricio, M., J. Pereira, J. Crisostomo, P. Matafome, M. Gomes, R. Seiça, and F. Caramelo. 2018. Using Resistin, glucose, age and BMI to predict the presence of breast cancer. BMC Cancer 18 (1):29–36. https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Coimbra#. doi:10.1186/s12885-017-3877-1.
  • Rezaei, A., M. Sharafi, J. Behboodian, and A. Zamani. 2018. Inferences on stress-strength parameter based on GLD5 distribution. Communications in Statistics - Simulation and Computation 47 (5):1251–63. doi:10.1080/03610918.2017.1309666.
  • Safariyan, A., M. Arashi, and R. A. Belaghi. 2019. Improved point and interval estimation of the stress-strength reliability based on ranked set sampling. Statistics 53 (1):101–25. doi:10.1080/02331888.2018.1547906.
  • Samawi, H. M., M. S. Ahmed, and W. A. Abu-Dayyeh. 1996. Estimating the population mean using extreme ranked set sampling. Biometrical Journal 38 (5):577–86. doi:10.1002/bimj.4710380506.
  • Samawi, H. M., H. Rochani, D. Linder, and A. Chatterjee. 2017. More efficient logistic analysis using moving extreme ranked set sampling. Journal of Applied Statistics 44 (4):753–66. doi:10.1080/02664763.2016.1182136.
  • Sengupta, S., and S. Mukhuti. 2008. Unbiased estimation of P(X > Y) using ranked set sampling data. Statistics 42 (3):223–30. doi:10.1080/02331880701823271.
  • Shaibu, A.-B., and H. A. Muttlak. 2002. A comparison of the maximum likelihood estimators under ranked set sampling some of its modifications. Applied Mathematics and Computation 129 (2–3):441–53. doi:10.1016/S0096-3003(01)00055-8.
  • Sharma, V. K. 2018. Bayesian analysis of head and neck cancer data using generalized inverse Lindley stress-strength reliability model. Communications in Statistics - Theory and Methods 47 (5):1155–80. doi:10.1080/03610926.2017.1316858.
  • Sharma, V. K., S. K. Singh, U. Singh, and F. Merovci. 2016. The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communications in Statistics - Theory and Methods 45 (19):5709–29. doi:10.1080/03610926.2014.948206.
  • Wolfe, D. A. 2012. Ranked Set Sampling: Its Relevance and Impact on Statistical Inference. ISRN Probability and Statistics 2012:1–33. doi:10.5402/2012/568385.
  • Zheng, G., and M. F. Al-Saleh. 2002. Modified maximum likelihood estimators based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54 (3):641–58. doi:10.1023/A:1022475413950.

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