Moments of order statistics from student's t-distribution

Student's t (and related) distributions play a significant role in both robustness studies and modelling certain types of data. This family of thick-tailed distributions range from the Cauchy through (essentially) the logistic to the normal. Order statistics, and their expected values, variances and covariances, from a standard Student's t are needed to calculate, e.g., Lloyd's BLUEs and for comparing efficiency and robustness properties of different estimators. Previously, numerical integration methods were required to evaluate these moments. The present work finds explicit formulae for the moments in terms of sums. These relatively simple formulae allow easy computation of parameter estimates and allow for simple means by which different models (based on changing tail thickness) can be studied.