Computation and verification of means, variances and covariances for large sample order statistics

Order statistics are widely used in reliability evaluation and life prediction. The numerical computation of means, variances and covariances of order statistics has been well solved for small sample, however, it has not yet been completely solved for large sample because of computation precision. Formulas of mean and variance of the first order statistic from extreme value distribution are derived in analytic form. Furthermore, simplified formulas of mean, variance and covariance of normal order statistics are also derived in particular cases. They offer the verification for numerical computation results. A large number of computations and verifications indicate that the speed and the precision of current computers are enough to satisfy the high-precision computation of means, variances and covariances for large sample order statistics. Some computation and verification results are presented.