Monotonicity properties of the gamma family of distributions

2020/12/25 by Pinelis, Iosif
#26D15 #33B20 #60E15 #62E15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.13578

Abstract

For real a>0, let X_a denote a random variable with the gamma distribution with parameters a and 1. Then \mathsf P(X_a-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.

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