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On The Distribution Of Order Statistics For A Random Sample Size

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  • D. Gupta
  • R. C. Gupta

Abstract

The distributions of the life lengths of a parallel and of a series system with a random number of components have been studied in reliability theory. In this paper we obtain the distributions of the i'th order statistics and the range, assuming the sample size to be random, with a generalized negative binomial, a generalized Poisson and a generalized logarithmic series distribution. The results of Raghunandanan and Patil (1972) follow immediately from our results.

Suggested Citation

  • D. Gupta & R. C. Gupta, 1984. "On The Distribution Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(1), pages 13-19, March.
    • Handle: RePEc:bla:stanee:v:38:y:1984:i:1:p:13-19
    DOI: 10.1111/j.1467-9574.1984.tb01092.x
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    Cited by:

    1. Zhao, Xufeng & Chen, Mingchih & Nakagawa, Toshio, 2016. "Replacement policies for a parallel system with shortage and excess costs," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 89-95.
    2. Shree Khare & Keven Roy, 2021. "Quantifying the Role of Occurrence Losses in Catastrophe Excess of Loss Reinsurance Pricing," Risks, MDPI, vol. 9(3), pages 1-40, March.
    3. Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    4. Abdel-Aty Y. & Franz J. & Mahmoud M. A. W., 2003. "Bayesian Predictions for Exponentially Distributed Failure Times With One Change-Point," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 195-207, January.
    5. Zeinhum F. Jaheen, 2001. "Bayesian prediction for the Burr model with outliers and Random sample size," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 217-230.
    6. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.

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