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Title: Bounded distributions place limits on skewness and larger moments
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewnessD3is bounded from below by a function of the coefficient of variation (CoV) δ as D3 > δ − 1/δ. The results are extended to any distribution that is bounded with minimum value xmin and/or bounded with maximum value xmax. We build on the results to provide bounds for kurtosis D4, and conjecture analogous bounds exists for higher statistical moments.  more » « less
Award ID(s):
2306371 2002815
PAR ID:
10511074
Author(s) / Creator(s):
;
Editor(s):
Balogun, Oluwafemi Samson
Publisher / Repository:
plos.org
Date Published:
Journal Name:
PLOS ONE
Volume:
19
Issue:
2
ISSN:
1932-6203
Page Range / eLocation ID:
e0297862
Subject(s) / Keyword(s):
statistics,skewness
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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