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THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES

Published online by Cambridge University Press:  31 March 2005

Karim M. Abadir
Karim M. Abadir
Affiliation:
University of York, UK
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Abstract

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.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 477 - 482
Copyright
© 2005 Cambridge University Press

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References

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