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Confidence intervals for quantiles based on samples of random sizes

Author

Listed:
  • Jazaa S. Al-Mutairi

    (Kuwait Institute for Scientific Research)

  • Mohammad Z. Raqab

    (Kuwait University
    King Abdulaziz University)

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.

Suggested Citation

  • Jazaa S. Al-Mutairi & Mohammad Z. Raqab, 2020. "Confidence intervals for quantiles based on samples of random sizes," Statistical Papers, Springer, vol. 61(1), pages 261-277, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0935-3
    DOI: 10.1007/s00362-017-0935-3
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    References listed on IDEAS

    as
    1. J. Ahmadi & N. Arghami, 2003. "Nonparametric confidence and tolerance intervals from record values data," Statistical Papers, Springer, vol. 44(4), pages 455-468, October.
    2. El-Adll, Magdy E., 2011. "Predicting future lifetime based on random number of three parameters Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1842-1854.
    3. J. M. Buhrman, 1973. "On order statistics when the sample size has a binomial distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 27(3), pages 125-126, September.
    4. K. Raghunandanan & S. A. Patil, 1972. "On order statistics for random sample size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 26(4), pages 121-126, December.
    5. Ahmadi, J. & Balakrishnan, N., 2004. "Confidence intervals for quantiles in terms of record range," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 395-405, July.
    6. Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
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    Cited by:

    1. Amany E. Aly, 2023. "Predictive inference of dual generalized order statistics from the inverse Weibull distribution," Statistical Papers, Springer, vol. 64(1), pages 139-160, February.
    2. Gerd Christoph & Vladimir V. Ulyanov, 2021. "Chebyshev–Edgeworth-Type Approximations for Statistics Based on Samples with Random Sizes," Mathematics, MDPI, vol. 9(7), pages 1-28, April.
    3. Gerd Christoph & Vladimir V. Ulyanov, 2020. "Second Order Expansions for High-Dimension Low-Sample-Size Data Statistics in Random Setting," Mathematics, MDPI, vol. 8(7), pages 1-28, July.
    4. Saadati Nik, A. & Asgharzadeh, A. & Raqab, Mohammad Z., 2021. "Estimation and prediction for a new Pareto-type distribution under progressive type-II censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 508-530.

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