This paper develops explicit closed formulas for the covariances of order statistics in samples from the extreme-value distribution which involve only tabulated functions. Such results do not appear to have been given previously. They have been used in an investigation of the estimation of extreme-value parameters by means of order statistics which will be presented in a fuller report to be submitted to the National Advisory Committee for Aeronautics.
Julius Lieblein. "On the Exact Evaluation of the Variances and Covariances of Order Statistics in Samples from the Extreme-Value Distribution." Ann. Math. Statist. 24 (2) 282 - 287, June, 1953. https://doi.org/10.1214/aoms/1177729034