Estimation of Asymptotic Pareto Laws and the Tail of a Distribution.

摘要

Stable and Pareto distributions provide good models, explaining various economic and other empirical variables. This research attempts to summarize and compare the existing methods for the parameter estimation of stable distributions and develop a new method of parameter estimation for the upper tail of Pareto distributions. Particular emphasis will be placed on the method of estimation which utilizes only the portion of the data consisting of sample values greater than a specified number. Quantile functions and associated theory is used to achieve the new method of probability estimation. A limited simulation study describing the properties and comparing these estimators with other well known estimators is undertaken.