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Entropy of Some Discrete Distributions

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Abstract

Cheraghchi [IEEE Transactions on Information Theory, 65, 2019, 3999-4009] derived expressions for the entropy for some basic discrete distributions. Not all of the expressions provided were in closed form. In this note, we derive closed form expressions for the entropy for more than ten flexible classes of distributions. The correctness of the expressions is checked numerically.

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References

  • Aksenov SV, Savageau MA (2005) Some properties of the Lerch family of discrete distributions. arXiv

  • Al-Babtain AA, Ahmed AHN, Afify AZ (2020) A new discrete analog of the continuous Lindley distribution, with reliability applications. Entropy. https://doi.org/10.3390/e2206060

    Article  MathSciNet  Google Scholar 

  • Al-Babtain AA, Elbatal I, Chesneau C, Elgarhy M (2021) Estimation of different types of entropies for the Kumaraswamy distribution. PLoS ONE. https://doi.org/10.1371/journal.pone.0249027

    Article  MATH  Google Scholar 

  • Cheraghchi M (2019) Expressions for the entropy of basic discrete distributions. IEEE Trans Inf Theory 65:3999–4009

    Article  MathSciNet  MATH  Google Scholar 

  • Conway RW, Maxwell WL (1962) A queuing model with state dependent service rates. J Ind Eng 12:132–136

    Google Scholar 

  • Daly F, Gaunt RE (2016) The Conway-Maxwell-Poisson distribution: Distributional theory and approximation. ALEA Lat Am J Probab Math Stat 13:635–658

    Article  MathSciNet  MATH  Google Scholar 

  • Garg M, Jain K, Kalla SL (2008) A further study of general Hurwitz-Lerch zeta function. Algebras Group Geom 25:311–319

    MathSciNet  MATH  Google Scholar 

  • Hassan A, Shalbaf GA, Bilal S, Rashid A (2020) A new flexible discrete distribution with applications to count data. Journal of Statistical Theory and Applications 19:102–108

    Google Scholar 

  • Inusah S, Kozubowski TJ (2006) A discrete analogue of the Laplace distribution. Journal of Statistical Planning and Inference 136:1090–1102

    Article  MathSciNet  MATH  Google Scholar 

  • Johnson N, Kemp A, Kotz S (2005) Univariate Discrete Distributions, 3rd edn. John Wiley and Sons Inc, Hoboken, New Jersey

    Book  MATH  Google Scholar 

  • Knessl C (1998) Integral representations and asymptotic expansions for Shannon and Rényi entropies. Appl Math Lett 11:69–74

    Article  MathSciNet  MATH  Google Scholar 

  • Kozubowski TJ, Inusah S (2006) A skew Laplace distribution on integers. Ann Inst Stat Math 58:555–571

    Article  MathSciNet  MATH  Google Scholar 

  • Kulasekara KB, Tonkyn DW (1992) A new discrete distribution with application to survival, dispersal and dispersion. Communication in Statistics - Simulation and Computation 21:499–518

    Article  MathSciNet  MATH  Google Scholar 

  • Lai CD, Wang DQ (1995) A finite range discrete life distribution. Int J Reliab Qual Saf Eng 2:147–160

    Article  Google Scholar 

  • Lin S-D, Srivastava HM (2004) Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations. Appl Math Comput 154:725–733

    MathSciNet  MATH  Google Scholar 

  • Olver FWJ, Lozier DW, Boisvert RF, Clark CW (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, New York

    MATH  Google Scholar 

  • Prudnikov AP, Brychkov YuA, Marichev OI (1986) Integrals and Series, Elementary functions, vol 1. Taylor and Francis

    MATH  Google Scholar 

  • Turowski K, Jacquet P, Szpankowski W (2019) Asymptotics of entropy of the Dirichlet-multinomial distribution. In: Proceedings of the 2019 IEEE International Symposium on Information Theory

  • Yule GU (1924) A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. Philos Trans R Soc B 213:21–87

    Google Scholar 

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Acknowledgements

The authors would like to thank the Editor and the referee for careful reading and comments which improved the paper.

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Authors and Affiliations

  1. Medical University of Pleven, Pleven, Bulgaria

    Kosto Mitov

  2. University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

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  1. Kosto Mitov
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  2. Saralees Nadarajah
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Correspondence to Saralees Nadarajah.

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Mitov, K., Nadarajah, S. Entropy of Some Discrete Distributions. Methodol Comput Appl Probab 25, 2 (2023). https://doi.org/10.1007/s11009-023-09978-1

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  • DOI: https://doi.org/10.1007/s11009-023-09978-1

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