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On the nearness of record values to order statistics from Pitman’s measure of closeness

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Abstract

In the two-sample prediction problem, record values from the present sample may be used as predictors of order statistics from a future sample. In this paper, we investigate the nearness of record statistics (upper and lower) to order statistics from a location-scale family of distributions in the sense of Pitman closeness and discuss the corresponding monotonicity properties. We then determine the closest record value to a specific order statistic from a future sample. Even though in general it depends on the parent distribution, exact and explicit expressions are derived for the required probabilities in the case of exponential and uniform distributions, and some computational results are presented as well. Finally, we consider the mean squared error criterion and examine the corresponding results in the exponential case.

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Acknowledgments

The authors express their sincere thanks to two anonymous reviewers for their useful comments and suggestions which improved the presentation of the paper considerably. Ahmadi’s research was supported by a grant from Ferdowsi University of Mashhad, No. MS90224AHM.

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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. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    N. Balakrishnan

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  1. Jafar Ahmadi
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  2. N. Balakrishnan
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Correspondence to Jafar Ahmadi.

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Ahmadi, J., Balakrishnan, N. On the nearness of record values to order statistics from Pitman’s measure of closeness. Metrika 76, 521–541 (2013). https://doi.org/10.1007/s00184-012-0402-z

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