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

Author

Listed:
  • 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.)

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.

Suggested Citation

  • David A. Swanson & Jeff Tayman & T.M. Bryan, 2018. "A Note on Rescaling the Arithmetic Mean for Right-skewed Positive Distributions," Review of Economics & Finance, Better Advances Press, Canada, vol. 14, pages 17-24, November.
    • Handle: RePEc:bap:journl:180402
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    References listed on IDEAS

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    1. David Swanson & Jeff Tayman & Charles Barr, 2000. "A note on the measurement of accuracy for subnational demographic estimates," Demography, Springer;Population Association of America (PAA), vol. 37(2), pages 193-201, May.
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    Cited by:

    1. Jack Baker & David Swanson & Jeff Tayman, 2021. "The Accuracy of Hamilton–Perry Population Projections for Census Tracts in the United States," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 40(6), pages 1341-1354, December.

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    More about this item

    Keywords

    Asymmetric distribution; Box-Cox Power Transformation; Outlier; R-MEAN;
    All these keywords.

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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