Quantile estimation based on modified ranked set sampling schemes using Pitman closeness

References

• Ahmadi, J., and N. Balakrishnan. 2010. Pitman closeness of current records for location-scale families. Statistics & Probability Letters 80 (21-22):1577–83. doi:10.1016/j.spl.2010.06.010.
   Web of Science ®Google Scholar
• Ahmadi, J., and M. Z. Raqab. 2013. Comparison of order statistics in two-sample problem in the sense of Pitman closeness. Statistics 47 (4):729–43. doi:10.1080/02331888.2011.647916.
   Web of Science ®Google Scholar
• Al-Saleh, M. F., and A. I. Al-Omari. 2002. Multistage ranked set sampling. Journal of Statistical Planning and Inference 102 (2):273–86. doi:10.1016/S0378-3758(01)00086-6.
   Web of Science ®Google Scholar
• Al-Saleh, M. F., and M. H. Samuh. 2008. On multistage ranked set sampling for distribution and median estimation. Computational Statistics & Data Analysis 52 (4):2066–78. doi:10.1016/j.csda.2007.07.002.
   Web of Science ®Google Scholar
• Balakrishnan, N., K. Davies, and J. P. Keating. 2009. Pitman closeness of order statistics to population quantiles. Communications in Statistics - Simulation and Computation 38 (4):802–20. doi:10.1080/03610910802650313.
   Web of Science ®Google Scholar
• Balakrishnan, N., K. Davies, J. P. Keating, and R. L. Mason. 2010. Simultaneous closeness among order statistics to population quantiles. Journal of Statistical Planning and Inference 140 (9):2408–15. doi:10.1016/j.jspi.2010.02.013.
   Web of Science ®Google Scholar
• Balakrishnan, N., K. Davies, J. P. Keating, and R. L. Mason. 2011. Pitman closeness, monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under Type II censoring. Journal of Statistical Computation and Simulation 81 (8):985–99. doi:10.1080/00949651003587684.
   Web of Science ®Google Scholar
• Balakrishnan, N., K. Davies, J. P. Keating, and R. L. Mason. 2012. Pitman closeness of best linear unbiased and invariant predictors for exponential distribution in one- and two-sample situations. Communications in Statistics - Theory and Methods 41 (1):1–15. doi:10.1080/03610920903537301.
   Web of Science ®Google Scholar
• Balakrishnan, N., and T. Li. 2006. Confidence intervals for quantiles and tolerance intervals based on ordered ranked set samples. Annals of the Institute of Statistical Mathematics 58:757–77. doi:10.1007/s10463-006-0035-y.
   Google Scholar
• Barnett, V. 1999. Ranked set sample design for environmental investigations. Environmental and Ecological Statistics 6 (1):59–74. doi:10.1023/A:1009643517647.
   Web of Science ®Google Scholar
• Barnett, V., and K. Moore. 1997. Best linear unbiased estimates in ranked set sampling with particular reference to imperfect ordering. Journal of Applied Statistics 24 (6):697–710. doi:10.1080/02664769723431.
   Web of Science ®Google Scholar
• Blyth, C. R. 1972. Some probability paradoxes in choice from among random alternatives. Journal of the American Statistical Association 67 (338):366–81. doi:10.1080/01621459.1972.10482388.
   Google Scholar
• Chahkandi, M., J. Ahmadi, and S. Baratpour. 2014. Non-parametric prediction intervals for the lifetime of coherent systems. Statistical Papers 55 (4):1019–34. doi:10.1007/s00362-013-0549-3.
   Web of Science ®Google Scholar
• Chen, Z. 2000. The efficiency of ranked-set sampling relative to simple random sampling under multi-parameter families. Statistica Sinica 10:247–63.
   Web of Science ®Google Scholar
• Chen, Z., Z. Bai, and B. K. Sinha. 2004. Ranked set sampling theory and application. Lecture Notes in Statistics. Berlin Heidelberg: Springer.
   Google Scholar
• Chen, H., E. A. Stasny, and D. A. Wolfe. 2005. Ranked set sampling for efficient estimation of a population proportion. Statistics in Medicine 24 (21):3319–29. doi:10.1002/sim.2158.
   PubMed Web of Science ®Google Scholar
• David, H. A., and H. N. Nagaraja. 2003. Order Statistics. 3rd ed. New York: John Wiley & Sons.
   Google Scholar
• Fountain, R. L., J. P. Keating, and H. B. Maynard. 1996. The simultaneous comparison of estimators. Mathematical Methods of Statistics 5:187–98.
   Google Scholar
• Jafari Jozani, M., K. F. Davies, and N. Balakrishnan. 2012. Pitman closeness results concerning ranked set sampling. Statistics & Probability Letters 82 (12):2260–9. doi:10.1016/j.spl.2012.08.011.
   Web of Science ®Google Scholar
• Keating, J. P., R. L. Mason, and P. K. Sen. 1993. Pitman’s measure of closeness: A comparison of statistical estimators. Philadelphia: Society for Industrial and Applied Mathematics.
   Google Scholar
• Mahdizadeh, M., and N. R. Arghami. 2010. Efficiency of ranked set sampling in entropy estimation and goodness-of-fit testing for the inverse Gaussian law. Journal of Statistical Computation and Simulation 80 (7):761–74. doi:10.1080/00949650902773551.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Mirfarah, E., and J. Ahmadi. 2014. Pitman closeness of k-records from two sequences to progressive Type-II censored order statistics. Computational Statistics 29 (5):1279–300. doi:10.1007/s00180-014-0491-4.
   Web of Science ®Google Scholar
• Morabbi, H., M. Razmkhah, and J. Ahmadi. 2016a. Nonparametric confidence intervals for quantiles based on a modified ranked set sampling. Communications for Statistical Applications and Methods 23 (2):119–29. doi:10.5351/CSAM.2016.23.2.119.
   Web of Science ®Google Scholar
• Morabbi, H., M. Razmkhah, and J. Ahmadi. 2016b. Point estimation of lower quantiles based on two-sampling scheme. Communications in Statistics - Theory and Methods 45 (13):4018–34. doi:10.1080/03610926.2014.915044.
   Web of Science ®Google Scholar
• Ozturk, O., and J. V. Deshpande. 2006. Ranked-set sample nonparametric quantile confidence intervals. Journal of Statistical Planning and Inference 136 (3):570–7. doi:10.1016/j.jspi.2004.07.011.
   Web of Science ®Google Scholar
• Pitman, E. J. G. 1937. The closest estimates of statistical parameters. Mathematical Proceedings of the Cambridge Philosophical Society 33 (2):212–22. doi:10.1017/S0305004100019563.
   Google Scholar
• Proschan, F. 1963. Theoretical explanation of observed decreasing failure rate. Technometrics 5 (3):375–83. doi:10.1080/00401706.1963.10490105.
   Web of Science ®Google Scholar
• Razmkhah, M., and J. Ahmadi. 2013. Pitman closeness of current k-records to population quantiles. Statistics & Probability Letters 83 (1):148–56. doi:10.1016/j.spl.2012.08.010.
   Web of Science ®Google Scholar
• Robert, C. P., J. T. G. Hwang, and W. E. Strawderman. 1993. Is Pitman closeness a reasonable criterion? With comment and rejoinder. Journal of the American Statistical Association 88 (421):74–6. doi:10.2307/2290698.
   Web of Science ®Google Scholar
• Takahasi, K., and K. Wakimoto. 1968. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics 20 (1):1–31. doi:10.1007/BF02911622.
   Web of Science ®Google Scholar
• Volterman, W., K. F. Davies, and N. Balakrishnan. 2013. Simultaneous Pitman closeness of progressively type-II right-censored order statistics to population quantiles. Statistics 47 (2):439–52. doi:10.1080/02331888.2011.605890.
   Web of Science ®Google Scholar
• Wolfe, D. A. 2004. Ranked set sampling: An approach to more efficient data collection. Statistical Science 19 (4):636–43. doi:10.1214/088342304000000369.
   Web of Science ®Google Scholar
• Zhu, M., and Y.-G. Wang. 2005. Quantile estimation from ranked set sampling data. Sankhya Ser A 67:295–304.
   Google Scholar