Order statistics from the half logistic distribution

Let X be a random variable having a half logistic distribution, obtained by folding the logistic distribution. For this distribution, some recurrence relations are established for the moments and product moments of order statistics. Starting with the first k moments of X, it is noted that one can calculate the first k moments of all order statistics. Using these relations, we tabulate means, variances and covariances in samples of size n= 1(1)15. The modes of all order statistics and the percentage points of the extremes are also tabulated.