Monotonicity properties of the gamma family of distributions

Iosif Pinelis

Statistics & Probability Letters, 2021, vol. 171, issue C

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.

Keywords: Stochastic monotonicity; Gamma distribution; Incomplete gamma function; Logarithmic mean (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.109027

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