Geometric mean extension for data sets with zeros
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.
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