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On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution

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Abstract

In this work we prove that for an exchangeable multivariate normal distribution the joint distribution of a linear combination of order statistics and a linear combination of their concomitants together with an auxiliary variable is skew normal. We also investigate some special cases, thus extending the results of Olkin and Viana (J Am Stat Assoc 90:1373–1379, 1995), Loperfido (Test 17:370–380, 2008a) and Sheikhi and Jamalizadeh (Paper 52:885–892, 2011).

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Authors and Affiliations

  1. Department of Statistics, Shahid Bahonar University, Kerman, Iran

    Ayyub Sheikhi & Mahbanoo Tata

  2. Department of Statistics, University of Isfahan, Isfahan, Iran

    Yaser Mehrali

Authors
  1. Ayyub Sheikhi
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  2. Yaser Mehrali
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  3. Mahbanoo Tata
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Correspondence to Ayyub Sheikhi.

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Sheikhi, A., Mehrali, Y. & Tata, M. On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution. Stat Papers 54, 325–332 (2013). https://doi.org/10.1007/s00362-012-0430-9

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  • DOI: https://doi.org/10.1007/s00362-012-0430-9

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