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A nonparametric estimation of the entropy for absolutely continuous distributions (Corresp.)
Abstract
LetF(x)be an absolutely continuous distribution having a density functionf(x)with respect to the Lebesgue measure. The Shannon entropy is defined asH(f) = -\int f(x) \ln f(x) dx. In this correspondence we propose, based on a random sampleX_{1}, \cdots , X_{n}generated fromF, a nonparametric estimate ofH(f)given by\hat{H}(f) = -(l/n) \sum_{i = 1}^{n} \In \hat{f}(x), where\hat{f}(x)is the kernel estimate offdue to Rosenblatt and Parzen. Regularity conditions are obtained under which the first and second mean consistencies of\hat{H}(f)are established. These conditions are mild and easily satisfied. Examples, such as Gamma, Weibull, and normal distributions, are considered.
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Cited by
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Metadata
- Authors
- Ahmad, I., & Lin, P.-E.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1976-05
- Volume
- 22
- Issue
- 3
- Pages
- 372-375
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2086839920
- Cited by
- 199
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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