Geometric mean extension for data sets with zeros

06/17/2018

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by   Roberto de la Cruz, et al.

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There are numerous examples in different research fields where the use of the geometric mean is more appropriate than the arithmetic mean. Nevertheless, the geometric mean has a serious limitation in comparison with the arithmetic mean. Means are used to summarize the information in a large set of values in a single number; however, the geometric mean of a data set with at least one zero is always zero, as a result, the geometric mean does not capture any information about the non-zero values. The purpose of this short contribution is to review solutions proposed in the literature and their issues, followed by the formulation of a modified version of the geometric mean that can handle zeros while satisfying recovery + monotonicity properties.