THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES
Let x be a random variable whose first three moments exist. If the density of x is unimodal and positively skewed, then counterexamples are provided which show that the inequality mode ≤ median ≤ mean does not necessarily hold.I thank Andrey Vasnev for help with the graphs and Jan Magnus for various...
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Veröffentlicht in: | Econometric theory 2005-04, Vol.21 (2), p.477-482 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Let x be a random variable whose first three moments exist.
If the density of x is unimodal and positively skewed, then
counterexamples are provided which show that the inequality mode ≤
median ≤ mean does not necessarily hold.I thank Andrey Vasnev for help with the graphs and Jan Magnus
for various helpful discussions. I also thank Martin Bland, Paolo Paruolo,
Peter Phillips, Michael Rockinger, and a referee for their comments. ESRC
grant R000239538 is gratefully acknowledged. |
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ISSN: | 0266-4666 1469-4360 |
DOI: | 10.1017/S0266466605050267 |