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Sharp estimates for the median of the [Gamma](n+1,1) distribution

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  • Adell, José A.
  • Jodrá, Pedro

Abstract

We give sharp upper and lower bounds for the median of the [Gamma](n+1,1) distribution, thus providing an immediate proof of two conjectures by Chen and Rubin (Statist. Probab. Lett. 4 (1986) 281) referring to the median of the Poisson distribution. Our approach uses a differential calculus for nonnecessarily smooth functions of the standard Poisson process and the central limit theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:2:p:185-191
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    References listed on IDEAS

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    1. 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.
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