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Monotonicity properties of the gamma family of distributions

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  • Pinelis, Iosif

Abstract

For real a>0, let Xa denote a random variable with the gamma distribution with parameters a and 1. Then P(Xa−a>c) is increasing in a for each real c⩾0; non-increasing in a for each real c⩽−1∕3; and non-monotonic in a for each c∈(−1∕3,0). This extends and/or refines certain previously established results.

Suggested Citation

  • Pinelis, Iosif, 2021. "Monotonicity properties of the gamma family of distributions," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s0167715220303308
    DOI: 10.1016/j.spl.2020.109027
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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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    Cited by:

    1. 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.

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