Confidence intervals for the tail index of the Pareto distribution of the first type
MIN, BO YUN
Using pivotal quantities, we construct a variety of exact and asymptotic confidence intervals (CI) for the tail index (shape parameter) of the Pareto distribution of the first type assuming that the scale parameter is known. The obtained CI's are compared in terms of their expected lengths and finite-sample coverage probabilities, and thus the better performing CI's among them are determined. We also outline the construction of exact and asymptotic CI's for the tail index when the scale parameter is unknown.
Pareto distribution, Functional central limit theorem, Student process, Confidence interval, Generalized median estimator, Domain of attraction of the normal law