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arXiv · 2210.02848

The Shannon Entropy of a Histogram

Stephen Watts·Lisa Crow
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Abstract

The histogram is a key method for visualizing data and estimating the underlying probability distribution. Incorrect conclusions about the data result from over or under-binning. A new method based on the Shannon entropy of the histogram uses a simple formula based on the differential entropy estimated from nearest-neighbour distances. Links are made between the new method and other algorithms such as Scott's formula, and cost and risk function methods. A parameter is found that predicts over and under-binning, which can be estimated for any histogram. The new algorithm is shown to be robust by application to real data.

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Stephen Watts, Lisa Crow. 2022-10-06. The Shannon Entropy of a Histogram. https://arxiv.org/abs/2210.02848

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