ABSTRACT
From the expressions of the marginal and joint density functions of order statistics, the single and the product moments of order statistics can be computed by employing one- and two-dimensional numerical integration routines. Since the required integration cannot be performed algebraically, numerical integration techniques have been adopted. Specifically, the single integrals needed for the computation of the means and variances of order statistics were computed by using the Gaussian quadrature with 512 lattice points over differing lengths of intervals. Since the single integrals involved only finite lower limits, except in the case of the standard normal distribution, determination of an appropriate upper termination point for the integrals posed quite a challenge as it very much depended on the values of n, i and k. After determining the suitable upper termination points in each case by examining the cumulative distribution function, the Gaussian quadrature with 512 lattice points was employed for the computation of the single integrals.
