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Prediction in a trivariate normal distribution via a linear combination of order statistics

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  • Jamalizadeh, A.
  • Balakrishnan, N.

Abstract

In this paper, by considering a trivariate normal distribution, we derive the exact joint distribution of one variable and a linear combination of order statistics from the other two variables. We show that this joint distribution is a mixture of unified bivariate skew-normal distributions. This mixture form enables us to predict the variable based on a linear combination of order statistics from the other two variables. We finally illustrate the usefulness of these results by using a real-life data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:21:p:2289-2296
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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.

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