Open AccessOn the asymptotic distribution of an alternative measure of kurtosis
Author(s) -
Kagba Suaray
Publication year - 2015
Publication title -
international journal of advanced statistics and probability
Language(s) - English
Resource type - Journals
ISSN - 2307-9045
DOI - 10.14419/ijasp.v3i2.5007
Subject(s) - kurtosis , mathematics , measure (data warehouse) , statistics , moment (physics) , distribution (mathematics) , span (engineering) , mathematical analysis , computer science , physics , civil engineering , classical mechanics , database , engineering
Pearson defined the fourth standardized moment of a symmetric distribution as its kurtosis. There has been much discussion in the literature concerning both the meaning of kurtosis, as well as the effectiveness of the classical sample kurtosis as a reliable measure of peakedness and tail weight. In this paper, we consider an alternative measure, developed by Crow and Siddiqui, used to describe kurtosis. Its value is calculated for a number of common distributions, and a derivation of its asymptotic distribution is given. Simulations follow, which reveal an interesting connection to the literature on the ratio of normal random variables.