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

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, <CitationRef CitationID="CR15">1995</CitationRef>), Loperfido (Test 17:370–380, <CitationRef CitationID="CR11">2008a</CitationRef>) and Sheikhi and Jamalizadeh (Paper 52:885–892, <CitationRef CitationID="CR16">2011</CitationRef>). Copyright Springer-Verlag 2013