Abstract
On the basis of failure times of a sample of random size N of iid continuous random variables, we consider the estimation problem of population quantiles of the same distribution. Based on order statistics, confidence intervals for quantile intervals are introduced. Confidence intervals for the difference of quantiles are also investigated. Exact expressions for the coverage probabilities of these intervals are derived and computed numerically. A biometric data set representing the duration of remission of 20 Leukemia patients is used to illustrate the results developed here.
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References
Ahmadi J, Arghami NR (2003) Nonparametric confidence and tolerance intervals from record values data. Stat Pap 44:455–468
Ahmadi J, Balakrishnan N (2004) Confidence intervals for quantiles in terms of record range. Stat Probab Lett 68:395–405
Ahmadi J, Balakrishnan N (2005) Distribution-free confidence intervals for quantile intervals based on current records. Stat Probab Lett 75:190–202
Arnold BC, Balakrishnan N, Nagaraja HN (2008) A first course in order statistics, Classic edn. SIAM, Philadelphia
Barakat HM, El-Adll M, Aly AE (2014) Prediction intervals of future observations for a sample of random size from any continuous distribuiton. Math Comput Simul 97:1–13
Barakat HM, El-Adll M, Amany E Aly (2011) Exact prediction intervals for future exponential lifetime based on random generalized order statistics. Comput Math Appl 61(5):1366–1378
Barakat HM, Nigm EM, El-Adll ME, Yusuf M (2016) Prediction of future generalized order statistics based on exponential distribution with random sample size. Stat Pap. doi:10.1007/s00362-016-0779-2
Barlow RE, Proschan F (1981) Statistical theory of reliability and life testing. To begin with, Silver Spring
Basiri E, Ahmadi J, Raqab MZ (2015) Comparison among non-parametric prediction intervals of order statistics. Commun Stat 45(9):2699–2713
Buhrman JM (1973) On order statistics when the sample size has a binomial distribution. Stat Neerl 27:125–126
Danielak K (2005) Shapr upper bounds for expectations of differences of order statistics in various scale units. Commun Stat 33(4):787–803
David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, Hoboken
El-Adll ME (2011) Predicting future lifetime based on random number of three parameters Weibull distribution. Math Comput Simul 81:1824–1854
Fligner MA, Wolfe DA (1979) Nonparametric prediction intervals for a future sample developed distribution-free for a future sample median based on informative sample median. J Am Stat Assoc 74:453–456
Krewski D (1976) Distribution-free confidence intervals for quantile intervals. J Am Stat Assoc 71:420–422
Lawless JF (2003) Statistical models and methods for lifetime data. Wiley, New York
Nelson N (1982) Applied life data analysis. Wiley, New York
Raghunandanan K, Patil SA (1972) On order statistics for random sample size. Stat Neerl 26:121–126
Raqab MZ (2004) Evaluating improvements for spacings of order statistics. Extremes 6(3):259–273
Wilks SS (1962) Mathematical statistics. Wiley, New York
Wu FS, Wu CC (2005) Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. J Stat Plan Inference 134:392–408
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The authors would like to thank the referees for their comments and helpful suggestions.
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Al-Mutairi, J.S., Raqab, M.Z. Confidence intervals for quantiles based on samples of random sizes. Stat Papers 61, 261–277 (2020). https://doi.org/10.1007/s00362-017-0935-3
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DOI: https://doi.org/10.1007/s00362-017-0935-3
Keywords
- Order statistics
- Quantiles
- Probability coverage
- Random sample size
- Confidence intervals
- Outer and inner intervals
- Increments