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Dimensionality, Granularity, and Differential Residual Weighted Entropy
While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515354/ http://dx.doi.org/10.3390/e21090825 |
Sumario: | While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned quantity from their discrete summation origins, exploring the relationship between their absolute and differential forms, and thus derive a “differentialized” absolute entropy based on a chosen “working granularity” consistent with Buckingham’s [Formula: see text]-theorem. We apply this formulation to three common continuous distributions: exponential, Gaussian, and gamma and consider policies for optimizing the working granularity. |
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