Estimation of the Location and Scale Parameters of a Pareto Distribution by Linear Functions of Order Statistics

Given a random sample from a Pareto type distribution with the cdf F(x) = 1 — [1 + (x — α)/β]-y for x ≥ α, the problems of estimating (1) the scale parameter β when α and y are known, (2) the location parameter α when β and y are known, (3) α and β when y is known, are considered. Particular attention is given to the best linear unbiased estimates based on the complete sample and (for (1) and (3)) the asymptotically best linear unbiased estimates based on a few selected order statistics, but some alternative estimates are also considered. The problem of optimum spacing of the order statistics is solved analytically and numerically.