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Dergiler / Mathematical Sciences and Applications E-Notes / 2016 / Cilt: 4 - Sayı: 1

Renyi entropy in continuous case is not the limit of discrete case

M. Sanei TABASS
G. R. Mohtashami BORZADARAN
M. AMİNİ
Sayfa
113–117
Yayın Tarihi
2016-04-15
DOI
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Also, some notes are derived in view of the variate versions of entropy criteria.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Shannon entropy is the creation of Shannon (1948) based on the experiences in Bell System Company during and after the Second World War.
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Temel Bulgular & Veri:Then, Renyi (1961) generalized it for one parameter families of entropies.
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Sonuç & Katkı:Also, some notes are derived in view of the variate versions of entropy criteria.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Vector valued Dirichlet series (VVDS) · relative Ritt order · relative Ritt lower order

Abstract

Shannon entropy is the creation of Shannon (1948) based on the experiences in Bell System Company during and after the Second World War. Then, Renyi (1961) generalized it for one parameter families of entropies. This entropy for discrete random variables is non-negative but it can be negative in continuous case. In this paper, we show that Renyi entropy for continuous random variables is not equal to the limit of it for discrete random variables. Also, some notes are derived in view of the variate versions of entropy criteria.

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Bu Makaleye Atıf Yap

TABASS, M. S., BORZADARAN, G. R. M., AMİNİ, M. (2016). Renyi entropy in continuous case is not the limit of discrete case. Mathematical Sciences and Applications E-Notes, Cilt: 4 - Sayı: 1, 113–117. https://ajindex.com/articles/690764

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Kaynakça (14)

  1. Aczel, J. Forte, B. and Ng, C. T., Why Shannon and Hartley entropies are "natural". Adv. Appl. Probab. (1970), 6, 131-146
  2. Campbell, L.L., Exponential entropy as a measure of extent of a distribution. Zeitschr. fur Wahrsch. und verw. Geb. (1966), 5, 217-255
  3. Cover, T. M. and Thomas, J. A., Elements of Information Theory. Second Edition. Wiley Interscience. (2006)
  4. Daroczy, Z. and Maksa, Gy., Non-negative information functions in Analytic Function Methods in Probability and Statistics. Colloq. Math. Soc. J. Bolyai 21, Gyires, B., Ed; north Holand: Amesterdam. (1979), 65-76
  5. Diderrich, G., The role of boundedness in characterizing Shannon entropy. Information and Control. (1975), 29, 140-161
  6. Fadeev, D.K., On the concept of entropy of a finite probability scheme (in Russian). Uspehi Mat. Nauk. (1956), 11, 227-231
  7. Hartley, R. V. L., Transmission of information. Bell System Technical Journal. (1928), 7, 535-563
  8. Harvda, J. and Charvat, F., Quantification method of classification processes: Concept of structural α−entropy. Kybernetika. (1967), 3, 30-35
  9. Koski, T. and Persson, L.E., Some properties of generalized exponential entropies with applications to data compression. Information Theory. 50 (1992), 6, 1220-1228
  10. Lee, P. M., On the axioms of information theory. Ann. Math. Statist. (1964) 35, 415-418
  11. Renyi, A., On measures of entropy and information. Proc. Berekeley Symposium, Statist. Probability. (1961), 1, 547-561
  12. Shannon, C. E., A mathematical theory of communication. Bell System Technical Journal., (1948), 27, 379-423
  13. Tsallis, C., Possible generalizations of Boltzmann-Gibbs statistics. Journal of Statistical Physics. (1988), 52, 479-487
  14. Tverberg, H., A new derivation of the information function. Math. Scand. (1958), 6, 297-298.