THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES

Karim Abadir ()

Econometric Theory, 2005, vol. 21, issue 02, pages 477-482

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.

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