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Conditional properties of a random sample given an order statistic

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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.

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Acknowledgements

The authors would like to thank the two reviewers for their valuable comments to improve the quality of the paper. The original version of the paper was done while the first author was on sabbatical leave at The Ohio State University, Columbus. He is grateful for the hospitality of the College of Public Heath.

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Authors and Affiliations

  1. Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Jafar Ahmadi

  2. Division of Biostatistics, The Ohio State University, Columbus, OH, 43210, USA

    H. N. Nagaraja

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  1. Jafar Ahmadi
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  2. H. N. Nagaraja
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Correspondence to Jafar Ahmadi.

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Ahmadi, J., Nagaraja, H.N. Conditional properties of a random sample given an order statistic. Stat Papers 61, 1971–1996 (2020). https://doi.org/10.1007/s00362-018-1016-y

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  • DOI: https://doi.org/10.1007/s00362-018-1016-y

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