Simultaneous estimation of the location and scale parameters of the gamma distribution by linear functions of order statistics

Large sample estimation of the origin (α1 and the scale parameter (α2 of the gamma distribution when the shape parameter m is known is considered. Assuming both parameters are unknown, the optimum spacings (0<λ1<λ2<...λ k <1) determining the maximum efficiences among other choices of the same number of observations are obtained. The coefficients to be used in computing the estimates, their variances and their asymptotic relative efficiencies (A.R.E.) relative to the Cramer Rao lower bounds are given.