A review of more than one hundred Pareto-tail index estimators

This paper reviews more than one hundred Pareto (and equivalent) tail index estimators. It focuses on univariate estimators for nontruncated data. We discuss basic ideas of these estimators and provide their analytical expressions. As samples from heavy-tailed distributions are analysed by researchers from various fields of science, the paper provides nontechnical explanations of the methods, which could be understood by researchers with intermediate skills in statistics. We also discuss strengths and weaknesses of the estimators, if they are known. The paper can be viewed as a catalog or a reference book on Pareto-tail index estimators.