Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.02955 |
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Sommario:
- This article establishes necessary and sufficient conditions under which a finite set of Generalized Shannon's Entropy (GSE) characterizes a finite discrete distribution up to permutation. For an alphabet of cardinality K, it is shown that K-1 distinct positive real orders of GSE are sufficient (and necessary if no multiplicity) to identify the distribution up to permutation. When the distribution has a known multiplicity structure with s distinct values, s-1 orders are sufficient and necessary. These results provide a label-invariant foundation for inference on unordered sample spaces and enable practical goodness-of-fit procedures across disparate alphabets. The findings also suggest new approaches for testing, estimation, and model comparison in settings where moment-based and link-based methods are inadequate.