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Relationships between moments of two related sets of order statistics and some extensions

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Abstract

Govindarajulu expressed the moments of order statistics from a symmetric distribution in terms of those from its folded form. He derived these relations analytically by dividing the range of integration suitably into parts. In this paper, we establish these relations through probabilistic arguments which readily extend to the independent and non-identically distributed case. Results for random variables having arbitrary multivariate distributions are also derived.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, Ontario, Canada

    N. Balakrishnan

  2. Department of Statistics, University of Kentucky, 40506-0027, Lexington, KY, USA

    Z. Govindarajulu

  3. Indian Statistical Institute, SJS Sansanwal Marg, 110016, New Delhi, India

    K. Balasubramanian

Authors
  1. N. Balakrishnan
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  2. Z. Govindarajulu
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  3. K. Balasubramanian
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Additional information

The first author would like to thank the Natural Sciences and Engineering Research Council of Canada for funding this research.

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Balakrishnan, N., Govindarajulu, Z. & Balasubramanian, K. Relationships between moments of two related sets of order statistics and some extensions. Ann Inst Stat Math 45, 243–247 (1993). https://doi.org/10.1007/BF00775811

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  • DOI: https://doi.org/10.1007/BF00775811

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