Optimal estimation for the Pareto distribution
This paper proposes an optimal estimation method for the shape parameter, probability density function and upper tail probability of the Pareto distribution. The new method is based on a weighted empirical distribution function. The exact efficiency functions of the estimators relative to the existing estimators are derived. The paper gives L-1-optimal and L-2-optimal weights for the new weighted estimator. Monte Carlo simulation results confirm the theoretical conclusions. Both theoretical and simulation results show that the new estimation method is more efficient relative to several existing methods in many situations.
weighted empirical distribution function efficiency order statistics density estimation pareto upper tail