Abstract
We suggest a ranked set sample method to improve Bayesian prediction intervals. The paper deals with the Bayesian prediction intervals in the context of an ordered ranked set sample from a certain class of exponential-type distributions. A proper general prior density function is used and the predictive cumulative function is obtained in the two-sample case. The special case of linear exponential distributed observations is considered and completed with numerical results.
The author appreciates the comments of the referees and the editor which improved the first draft of this manuscript.
References
1 Y. Abdel-Aty, J. Franz and M. A. W. Mahmoud, Bayesian prediction based on generalized order statistics using multiply type II censored, Statistics 41 (2007), 6, 495–504. 10.1080/02331880701223357Search in Google Scholar
2 A. Adatia, Estimation of parameters of the half-logistic distribution using generalized ranked set sampling, Comput. Stat. Data Anal. 33 (2000), 1–13. 10.1016/S0167-9473(99)00035-3Search in Google Scholar
3 S. A. Al-Hadhrami, A. I. Al-Omari and M. F. Al-Saleh, Estimation of standard deviation of normal distribution using moving extreme ranked set sampling, Proc. World Acad. Sci. Eng. Technol. 37 (2009), 988–993. Search in Google Scholar
4 E. K. Al-Hussaini, Predicting observables from a general class of distributions, J. Statist. Plann. Inference 79 (1999), 1, 79–91. 10.1016/S0378-3758(98)00228-6Search in Google Scholar
5 M. T. Alodat and O. A. Al-Sagheer, Estimation the location and scale parameters using ranked set sampling, J. Appl. Statist. Sci. 15 (2007), 245–252. Search in Google Scholar
6 B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics, Wiley, New York, 1992. Search in Google Scholar
7 N. Balakrishnan, Permanents, order statistics, outliers and robustness, Rev. Mat. Complut. 20 (2008), 7–107. 10.5209/rev_REMA.2007.v20.n1.16528Search in Google Scholar
8 N. Balakrishnan and T. Li, Ordered ranked set samples and applications to inference, J. Stat. Plann. Inference 138 (2008), 3512–3524. 10.1016/j.jspi.2005.08.050Search in Google Scholar
9 N. Balakrishnan and A. R. Shafay, One-and two-sample Bayesian prediction intervals based on Type-II hybrid censored data, Comm. Statist. Theory Methods 41 (2012), 1511–1531. 10.1080/03610926.2010.543300Search in Google Scholar
10 J. M. Cobby, M. S. Ridout, P. J. Bassett and R. V. Large, An investigation into the use of ranked set sampling on grass and grass-clover swards, Grass Forage Sci. 40 (1985), 3, 257–263. 10.1111/j.1365-2494.1985.tb01753.xSearch in Google Scholar
11 H. A. David and H. N. Nagaraja, Order Statistics, 3rd ed., Wiley, New York, 2003. 10.1002/0471722162Search in Google Scholar
12 M. J. Evans, Application of ranked set sampling to regeneration surveys in areas direct-seeded to longleaf pine, Master's thesis, Louisiana State University, School of Forestry and Wildlife Management, Baton Rouge, 1967. Search in Google Scholar
13 A. C. Gleeson and C. A. McGilchrist, Bilateral processes on a reetangular lattice, Aust. J. Stat. 22 (1980), 197–206. 10.1111/j.1467-842X.1980.tb01167.xSearch in Google Scholar
14 L. S. Halls and T. R. Dell, Trial of ranked set sampling for forage yields, Forest Sci. 12 (1966), 1, 22–26. Search in Google Scholar
15 O. R. Jewiss, Shoot development and number, Sward Measurement Handbook, The British Grassland Society, Hurley (1981), 93–114. Search in Google Scholar
16 E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457–481. 10.1007/978-1-4612-4380-9_25Search in Google Scholar
17 W. L. Martin, T. Shank, G. Oderwald and D. W. Smith, Evaluation of ranked set sampling for estimating shrub phytomass in application Oak forest, Technical Report No. FWS-4-80, School of Forestry and Wildlife Recourses VPI & SU, Blackburg, 1980. Search in Google Scholar
18 G. A. McIntyre, A method for unbiased selective sampling using ranked sets, Austral. J. Agricultural Res. 3 (1952), 385–390. 10.1071/AR9520385Search in Google Scholar
19 M. M. Mohie El-Din, M. S. Kotb, E. F. Abd-Elfattah and H. A. Newer, Bayesian inference and prediction of the Pareto distribution based on ordered ranked set sampling, Comm. Statist. Theory Methods, to appear. Search in Google Scholar
20 M. M. Mohie El-Din, M. S. Kotb and H. A. Newer, Bayesian estimation and prediction for Pareto distribution based on ranked set sampling, J. Stat. Appl. Prob. 4 (2015), 2, 211–221. Search in Google Scholar
21 A. Sadek, K. S. Sultan and N. Balakrishnan, Bayesian estimation based on ranked set sampling using asymmetric loss function, Bull. Malays. Math. Sci. Soc. 38 (2015), 707–718. 10.1007/s40840-014-0045-5Search in Google Scholar
22 A. B. Shaibu and H. A. Muttlak, Estimating the parameters of normal, exponential and gamma distributions using median and extreme ranked set samples, Statistica 64 (2004), 1, 75–98. Search in Google Scholar
23 S. K. Sinha, B. K. Sinha and S. Purkayastha, On some aspects of ranked set sampling for estimation of normal and exponential parameters, Stat.Decisions 14 (1996), 223–240. 10.1524/strm.1996.14.3.223Search in Google Scholar
24 S. L. Stokes, Parametric ranked set sampling, Ann. Inst. Stat. Math. 47 (1995), 465–482. 10.1007/BF00773396Search in Google Scholar
25 K. Takahasi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Stat. Math. 20 (1968), 1–31. 10.1007/BF02911622Search in Google Scholar
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Checking Default Correlation and Score Correlation in a Breakpoint Model for Rating Classification
- An ARL-Unbiased np-Chart
- Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution
- New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution
- Bayesian Prediction Bounds for the Exponential-Type Distribution Based on Ordered Ranked Set Sampling
- Solving a Functional Equation and Characterizing Distributions by Quantile Past Lifetime Functions
Articles in the same Issue
- Frontmatter
- Checking Default Correlation and Score Correlation in a Breakpoint Model for Rating Classification
- An ARL-Unbiased np-Chart
- Design of Optimal Reliability Acceptance Sampling Plans for Exponential Distribution
- New Acceptance Sampling Plans Based on Percentiles for Exponentiated Fréchet Distribution
- Bayesian Prediction Bounds for the Exponential-Type Distribution Based on Ordered Ranked Set Sampling
- Solving a Functional Equation and Characterizing Distributions by Quantile Past Lifetime Functions