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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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  • Ayyub Sheikhi
  • Yaser Mehrali
  • Mahbanoo Tata

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 ). Copyright Springer-Verlag 2013

Suggested Citation

  • Ayyub Sheikhi & Yaser Mehrali & Mahbanoo Tata, 2013. "On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution," Statistical Papers, Springer, vol. 54(2), pages 325-332, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:325-332
    DOI: 10.1007/s00362-012-0430-9
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    References listed on IDEAS

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    1. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2007. "On the exact distribution of linear combinations of order statistics from dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1876-1894, November.
    2. Alan Hutson, 2009. "A distribution function estimator for the difference of order statistics from two independent samples," Statistical Papers, Springer, vol. 50(1), pages 203-208, January.
    3. Nicola Loperfido, 2008. "Modeling maxima of longitudinal contralateral observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 370-380, August.
    4. Ayyub Sheikhi & Ahad Jamalizadeh, 2011. "Regression analysis using order statistics," Statistical Papers, Springer, vol. 52(4), pages 885-892, November.
    5. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    6. Loperfido, Nicola, 2008. "A note on skew-elliptical distributions and linear functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3184-3186, December.
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    Cited by:

    1. Hui Jiang & Jin Shao & Qingshan Yang, 2021. "Sharp large deviations for a class of normalized L-statistics and applications," Statistical Papers, Springer, vol. 62(2), pages 721-744, April.

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