Measuring heavy-tailedness of distributions

TL;DR

This paper introduces a new measure for heavy-tailedness of distributions, aiding in classification and analysis of extreme values, and proposes extremal index estimators based on this measure.

Contribution

It proposes a novel measure for heavy-tailedness, enabling distribution classification and improved extremal index estimation.

Findings

New heavy-tailedness measure introduced

Distribution classification based on heavy-tailedness developed

Extremal index estimators proposed and partially analyzed

Abstract

Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed distribution. The difficulties with their usage are usually related to the estimation of the tail index in case it exists. There are many measures for the center of the distribution, e.g. mean, mode, median. There are many measures of the variance, asymmetry, and kurtosis, but there is no easy characteristic for heavy-tailedness of the observed distribution. Here we propose such a measure, give some examples and explore some of its properties. This allows us to introduce a classification of the distributions, with respect to their heavy-tailedness. The idea is to help and navigate practitioners for accurate and easier work in the field of probability distributions. Using the properties of the defined characteristics some distribution sensitive extremal index estimators are proposed and their properties are partially investigated.