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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| container_title | Econometric theory |
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| creator | Abadir, Karim M. |
| description | 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. |
| doi_str_mv | 10.1017/S0266466605050267 |
| format | Article |
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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
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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.</description><subject>Counterexamples</subject><subject>Econometrics</subject><subject>Inequality</subject><subject>Mathematical analysis</subject><subject>Mathematical methods</subject><subject>NOTES AND PROBLEMS</subject><subject>Random variables</subject><subject>Skewed distribution</subject><subject>Skewness</subject><subject>Statistical median</subject><subject>Statistical 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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.</abstract><cop>New York, USA</cop><pub>Cambridge University Press</pub><doi>10.1017/S0266466605050267</doi><tpages>6</tpages></addata></record> |
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| ispartof | Econometric theory, 2005-04, Vol.21 (2), p.477-482 |
| issn | 0266-4666 1469-4360 |
| language | eng |
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| source | JSTOR Archive Collection A-Z Listing; Cambridge University Press Journals Complete |
| subjects | Counterexamples Econometrics Inequality Mathematical analysis Mathematical methods NOTES AND PROBLEMS Random variables Skewed distribution Skewness Statistical median Statistical mode Studies |
| title | THE MEAN-MEDIAN-MODE INEQUALITY: COUNTEREXAMPLES |
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