Abstract
In this article, we study the joint distribution of X and two linear combinations of order statistics, a T Y (2) and b T Y (2), where a = (a 1, a 2)T and b = (b 1, b 2)T are arbitrary vectors in R 2 and Y (2) = (Y (1), Y (2))T is a vector of ordered statistics obtained from (Y 1, Y 2)T when (X, Y 1, Y 2)T follows a trivariate normal distribution with a positive definite covariance matrix. We show that this distribution belongs to the skew-normal family and hence our work is a generalization of Olkin and Viana (J Am Stat Assoc 90:1373–1379, 1995) and Loperfido (Test 17:370–380, 2008).
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Sheikhi, A., Jamalizadeh, A. Regression analysis using order statistics. Stat Papers 52, 885–892 (2011). https://doi.org/10.1007/s00362-009-0294-9
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DOI: https://doi.org/10.1007/s00362-009-0294-9