Comparing the Sample Mean and the Sample Median: An Exploration in the Exponential Power Family
- 1 February 1997
- journal article
- research article
- Published by Taylor & Francis in The American Statistician
- Vol. 51 (1) , 52-54
- https://doi.org/10.1080/00031305.1997.10473589
Abstract
We compare the (asymptotic) efficiencies of the sample mean and the sample median in the exponential power family. This single family of densities is an ideal one to illustrate the effect of “heavy tails” on the two estimators. We find the density for which the mean and median are equally efficient, and observe what happens for limiting cases within the family. Only basic tools are needed in the analysis and statistical development.Keywords
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