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On The Distributions Of Order Statistics For A Random Sample Size

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  • P.C. Consul

Abstract

The probability distribution of the i –th and j–th order statistics and of the range R of a sample of size n, taken from a population with probability density function f (x) have been obtained when the sample size n is a random variable N and has: (i) a generalized Poisson distribution; and (ii) a generalized negative bonimial distribution. Specific results are then obtained; (a) when f (x) is uniform over (0,1); and (b) when f(x) is exponential. All the results for N, being a Poisson, binomial and negative binomial rv follow as special cases.

Suggested Citation

  • P.C. Consul, 1984. "On The Distributions Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(4), pages 249-256, December.
    • Handle: RePEc:bla:stanee:v:38:y:1984:i:4:p:249-256
    DOI: 10.1111/j.1467-9574.1984.tb01115.x
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    Cited by:

    1. Bobotas, Panayiotis & Koutras, Markos V., 2024. "On the preservation of ageing properties under random maxima," Statistics & Probability Letters, Elsevier, vol. 210(C).
    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. 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.
    4. Nil Kamal Hazra & Asok K. Nanda & Moshe Shaked, 2014. "Some aging properties of parallel and series systems with a random number of components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 238-243, April.
    5. 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.

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