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Conditional properties of a random sample given an order statistic

Author

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  • Jafar Ahmadi

    (Ferdowsi University of Mashhad)

  • H. N. Nagaraja

    (The Ohio State University)

Abstract

This paper deals with the conditional properties of unordered observations in a random sample given the ith order statistic of the same sample. A characterization of symmetric distribution is given based on the properties of conditional moments. It is proved that the joint distribution has negative quadrant dependence structure and an exact expression for the Pearson correlation coefficient is given. Stochastic ordering results are obtained and it is shown that some orderings are inherited by the conditional distribution of the sample values. The results are useful in studying the properties of component lifetimes of a system with n components given the ith failure time and associated repair costs.

Suggested Citation

  • Jafar Ahmadi & H. N. Nagaraja, 2020. "Conditional properties of a random sample given an order statistic," Statistical Papers, Springer, vol. 61(5), pages 1971-1996, October.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:5:d:10.1007_s00362-018-1016-y
    DOI: 10.1007/s00362-018-1016-y
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    References listed on IDEAS

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    1. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. Afshin Parvardeh, 2015. "A note on the asymptotic distribution of the estimation of the mean past lifetime," Statistical Papers, Springer, vol. 56(1), pages 205-215, February.
    3. Serkan Eryılmaz, 2013. "On residual lifetime of coherent systems after the rth failure," Statistical Papers, Springer, vol. 54(1), pages 243-250, February.
    4. Iliopoulos, G. & Balakrishnan, N., 2009. "Conditional independence of blocked ordered data," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1008-1015, April.
    5. Shaomin Wu & Frank P. A. Coolen & Bin Liu, 2017. "Optimization of maintenance policy under parameter uncertainty using portfolio theory," IISE Transactions, Taylor & Francis Journals, vol. 49(7), pages 711-721, July.
    6. Mahdy, Mervat, 2016. "Further results related to variance past lifetime class & associated orderings and their properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1148-1160.
    7. Wen-Chuan Lee & Jong-Wuu Wu & Chun-Te Li, 2011. "Characterization of the mixtures of Rayleigh distributions by conditional expectation of order statistics," Statistical Papers, Springer, vol. 52(3), pages 657-675, August.
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    Cited by:

    1. Jorge Navarro & Camilla Calì & Maria Longobardi & Fabrizio Durante, 2022. "Distortion representations of multivariate distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 925-954, October.

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