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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

REFERENCES

Abadir, K.M. & M. Rockinger (2003) Density functionals, with an option-pricing application. Econometric Theory 19, 778–811.Google Scholar
Abdous, B. & R. Theodorescu (1998) Mean, median, mode IV. Statistica Neerlandica 52, 356–359.Google Scholar
Dharmadhikari, S.W. & K. Joag-Dev (1983) Mean, median, mode III. Statistica Neerlandica 37, 165–168.Google Scholar
Groeneveld, R.A. & G. Meeden (1977) The mode, median, and mean inequality. American Statistician 31, 120–121.Google Scholar
Kendall, M. & A. Stuart (1977) The Advanced Theory of Statistics, vol. 1, 4th ed. Charles Griffin & Co.
Runnenburg, J.Th. (1978) Mean, median, mode. Statistica Neerlandica 32, 73–79.Google Scholar
Zwet, W.R. van (1979) Mean, median, mode II. Statistica Neerlandica 33, 1–5.Google Scholar