A proposal of new disnormality indexes

Abstract

In this paper, well known disnormality or kurtosis indexes are decomposed into contributions to the measure of disnormality of the center, sides and tails of distributions. The results of this study confirm that the above indexes measure mainly the length and thickness of distribution tails at the expense of the distribution center, which may be more or less peaked or flat. The nature of this decomposition suggests the adoption of new and more appropriate measures of disnormality to capture the various forms in which disnormality occurs. The purpose is to put forward new indexes which are able to measure the aspects of disnormality more appropriately. The proposed indexes are less biased when compared to the structure of well-known indexes and are able to value not only the tail characteristics of distributions, but also those of the sides and the center.

Keywords:

• Disnormality
• indexes decomposition
• peakedness
• continuous distributions
• symmetric distributions
• new disnormality indexes