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Prediction of future generalized order statistics based on exponential distribution with random sample size

Author

Listed:
  • H. M. Barakat

    (Zagazig University)

  • E. M. Nigm

    (Zagazig University)

  • Magdy E. El-Adll

    (Helwan University)

  • M. Yusuf

    (Helwan University)

Abstract

In this paper we develop two pivotal quantities to construct prediction intervals for future two-parameter exponential lifetimes based on a random number of generalized order statistics (gOs) under a general set-up including progressive type II censored order statistics (pOs) with general scheme. Moreover, the expected value as well as the mean square error for the upper limit of predictive confidence interval (PCI) are obtained. Furthermore, a maximum likelihood predictor (MLP) for future exponential lifetimes is derived when the sample size is deterministic or random. Finally, a simulation study and an application to real data illustrate and corroborate the theoretical results.

Suggested Citation

  • H. M. Barakat & E. M. Nigm & Magdy E. El-Adll & M. Yusuf, 2018. "Prediction of future generalized order statistics based on exponential distribution with random sample size," Statistical Papers, Springer, vol. 59(2), pages 605-631, June.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0779-2
    DOI: 10.1007/s00362-016-0779-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. M. Mahmoud & H. Al-Nagar, 2009. "On generalized order statistics from linear exponential distribution and its characterization," Statistical Papers, Springer, vol. 50(2), pages 407-418, March.
    4. Félix Belzunce & Carolina Martínez-Riquelme, 2015. "Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders," Statistical Papers, Springer, vol. 56(4), pages 1175-1190, November.
    5. 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.
    6. Barakat, H.M. & El-Adll, Magdy E., 2009. "Asymptotic theory of extreme dual generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1252-1259, May.
    7. Chien-Tai Lin & N. Balakrishnan, 2003. "Exact prediction intervals for exponential distributions based on doubly Type-II censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(7), pages 783-801.
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    Cited by:

    1. H. M. Barakat & Haidy A. Newer, 2022. "Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size," Statistical Papers, Springer, vol. 63(6), pages 1801-1827, December.
    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. Tzong-Ru Tsai & Yuhlong Lio & Hua Xin & Hoang Pham, 2021. "Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution," Mathematics, MDPI, vol. 9(8), pages 1-17, April.

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