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Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations

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  • Balakrishnan, N.

Abstract

In this paper, we consider n independent observations from a multivariate normal distribution and discuss the multivariate order statistics induced by ordering linear combinations of the components observed. Specifically, we derive means, variances and covariances of the induced multivariate order statistics; these quantities are expressed in terms of the means, variances and covariances of standard normal order statistics which have been tabulated quite extensively. These generalize the recent results of Song (1992) based on independent normal variables.

Suggested Citation

  • Balakrishnan, N., 1993. "Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 343-350, August.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:5:p:343-350
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    Cited by:

    1. Jamalizadeh, A. & Balakrishnan, N. & Salehi, Mehdi, 2010. "Order statistics and linear combination of order statistics arising from a bivariate selection normal distribution," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 445-451, March.
    2. Jamalizadeh, A. & Mehrali, Y. & Balakrishnan, N., 2009. "Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4018-4027, October.
    3. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    4. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jos Mara, 2009. "Multivariate order statistics via multivariate concomitants," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 946-951, May.
    5. Jamalizadeh, A. & Balakrishnan, N., 2009. "Prediction in a trivariate normal distribution via a linear combination of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2289-2296, November.
    6. R. Arellano-Valle & Ahad Jamalizadeh & H. Mahmoodian & N. Balakrishnan, 2014. "$$L$$ L -statistics from multivariate unified skew-elliptical distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 559-583, May.

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