Estimators Based on Order Statistics from a Pareto Distribution

Abstract

Given a random sample from a Pareto distribution with the cdf F(x) = 1 − (1 + (x − α)/β)^-γ for x ≥ α, the problems of estimating (1) the scale parameter β when α and γ are known, (2) the location parameter α when β and γ are known, and (3) α and β when γ is known, are considered. The best linear unbiased estimators based on k selected order statistics are derived. Some special cases are considered in detail. A useful summation formula for ratios of gamma function-expressions is given.