Strong Asymmetry and the Mode, Median, and Mean Inequality
Keywords:skewness, Mode-Median-Mean inequality, Measures of dispersion
This paper introduces the consoled strong asymmetry and variation coefficient as generalizations of the standard measures of Pearson skewness coefficient and variance. Using these new measures, the concept of strong asymmetry is introduced. We prove that the median-mean inequality is valid for that kind of distribution, but even in that case, there is no relation between mode and median. A property similar to first-order stochastic dominance is proved for the variation coefficient. We also discuss the implications of that concept into economics.
Abadir, K. M. “The mean-median-mode inequality: counterexamples”. Econometric Theory 21 (2), 477–482. 2005.
Basu, S. and A. DasGupt. “The mean, median, and mode of unimodal distributions: a characterization”. Theory of Probability & Its Applications 41 (2), 210–223. 1995
Bell, D. E. “Disappointment in decision making under uncertainty”. Operations Research 33 (1), 1–27. 1995
Bickel, P. J. and E. L. Lehmann. “Descriptive statistics for nonparametric models. iii. Dispersion”. The Annals of Statistics 4 (6), 1139–1158. 1976
Gul, F. “A theory of disappointment aversion”. Econometrica: Journal of the conometric Society, 667–686. 1991
Kahneman, D., J. L. Knetsch, and R. H. Thaler. “Anomalies: The endowment effect, loss aversion, and status quo bias”. Journal of Economic Perspectives 5 (1), 193–206. 1991
Kahneman, D. and A. Tversky. “Prospect theory: An analysis of decision under risk”. Econometrica 47 (2), 263–292. 1979.
Loomes, G. and R. Sugden. “Disappointment and dynamic consistency in choice under uncertainty”. The Review of Economic Studies 53 (2), 271–282. 1986
Oja, H. “On location, scale, skewness and kurtosis of univariate distributions”. Scandinavian Journal of statistics, 154–168. 1981
VanZwet, W. R. “Convex transformations of random variables”. MC Tracts. 1970
Zwet, W. “Mean, median, mode ii”. Statistica Neerlandica 33, 1 – 5. 1979
How to Cite
Copyright (c) 2022 American Academic Scientific Research Journal for Engineering, Technology, and Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who submit papers with this journal agree to the following terms.