Title

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.

Publisher's Statement

© 2020 Elsevier B.V. Publisher’s version of record: https://doi.org/10.1016/j.spl.2020.109027

Publication Title

Statistics and Probability Letters

Share

COinS