Monotonicity properties of the gamma family of distributions
Document Type
Article
Publication Date
4-2021
Department
Department of Mathematical Sciences
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.
Publication Title
Statistics and Probability Letters
Recommended Citation
Pinelis, I.
(2021).
Monotonicity properties of the gamma family of distributions.
Statistics and Probability Letters,
171.
http://doi.org/10.1016/j.spl.2020.109027
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/14586
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Publisher's Statement
© 2020 Elsevier B.V. Publisher’s version of record: https://doi.org/10.1016/j.spl.2020.109027