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A Note on Rescaling the Arithmetic Mean for Right-skewed Positive Distributions

David A. Swanson (), Jeff Tayman () and T.M. Bryan ()
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David A. Swanson: Department of Sociology, University of California Riverside, U.S.A.
Jeff Tayman: Department of Economics, University of California San Diego, U.S.A.
T.M. Bryan: McKibben Demographic Research, U.S.A.

Review of Economics & Finance, 2018, vol. 14, 17-24

Abstract: When the arithmetic mean (mean) is used as a measure of location for a set of rightskewed positive observations, it is subject to being pulled upward. This upward movement tends to move the mean away from the bulk of the observations, making it less representative of them. One way to deal with this loss of representativeness is to transform the data. A Box-Cox power transformation can make a right-skewed distribution more symmetrical and then a measure of location for the original observations is found by applying an inverse transformation to the center of the transformed data. This approach was used in a series of papers dealing with the Mean Absolute Percent Error (MAPE) as a measure of forecast and estimation error. In this paper, we show that the Box-Cox power transformation can be used more generally with any mean computed for a set of right-skewed positive observations to develop R-MEAN (Rescaled-Mean). We provide a set of examples to illustrate this approach and show its use in an actual application.

Keywords: Asymmetric distribution; Box-Cox Power Transformation; Outlier; R-MEAN (search for similar items in EconPapers)
JEL-codes: B41 C13 C18 (search for similar items in EconPapers)
Date: 2018
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