Monotonicity properties of the gamma family of distributions
Department of Mathematical Sciences
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.
Statistics and Probability Letters
Monotonicity properties of the gamma family of distributions.
Statistics and Probability Letters,
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