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Bounds for the difference between median and mean of gamma and poisson distributions

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  • Chen, Jeesen
  • Rubin, Herman

Abstract

We use elementary methods and the Poisson-Gamma relationship to obtain bounds for the difference between median and mean of Gamma and Poisson distributions.

Suggested Citation

  • Chen, Jeesen & Rubin, Herman, 1986. "Bounds for the difference between median and mean of gamma and poisson distributions," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 281-283, October.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:6:p:281-283
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    Cited by:

    1. Alexander Katzur & Udo Kamps, 2020. "Classification using sequential order statistics," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 201-230, March.
    2. Frédéric Ouimet, 2023. "A refined continuity correction for the negative binomial distribution and asymptotics of the median," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 827-849, October.
    3. Pinelis, Iosif, 2021. "Monotonicity properties of the gamma family of distributions," Statistics & Probability Letters, Elsevier, vol. 171(C).
    4. Alzer, Horst, 2006. "A convexity property of the median of the gamma distribution," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1510-1513, August.
    5. Deligiannis, Michalis & Liberopoulos, George & Benioudakis, Myron, 2023. "Dynamic supplier competition and cooperation for buyer loyalty on service," International Journal of Production Economics, Elsevier, vol. 255(C).
    6. Phillips, Peter C.B. & Gao, Wayne Yuan, 2017. "Structural inference from reduced forms with many instruments," Journal of Econometrics, Elsevier, vol. 199(2), pages 96-116.
    7. Noorizadegan, Mahdi & Chen, Bo, 2018. "Vehicle routing with probabilistic capacity constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 544-555.
    8. Ding, S. & Koole, G. & van der Mei, R.D., 2015. "On the estimation of the true demand in call centers with redials and reconnects," European Journal of Operational Research, Elsevier, vol. 246(1), pages 250-262.
    9. Noguchi, Kimihiro & Ward, Mayla C., 2024. "Asymptotic optimality of the square-root transformation on the gamma distribution using the Kullback–Leibler information number criterion," Statistics & Probability Letters, Elsevier, vol. 210(C).
    10. Richard F Lyon, 2021. "On closed-form tight bounds and approximations for the median of a gamma distribution," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-18, May.
    11. Adell, José A. & Jodrá, Pedro, 2005. "Sharp estimates for the median of the [Gamma](n+1,1) distribution," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 185-191, February.
    12. Jean-François Coeurjolly & Joëlle Rousseau Trépanier, 2020. "The median of a jittered Poisson distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 837-851, October.

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