伽玛分布族的单调性
Monotonicity properties of the gamma family of distributions
摘要：
对于实数$a>0$，令$X_a$表示具有参数$a$和$1$的Γ分布的随机变量。则对于每个实数$c\ge0$，$\mathsf P(X_a-a>c)$在$a$中递增;对于每个实数$c\le-1/3$，$a$中不递增;对于每个$c\in(-1/3,0)$，$a$中非单调。这扩展和/或改进了某些先前建立的结果。
英文摘要：
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 $c\ge0$; non-increasing in $a$ for each real $c\le-1/3$; and non-monotonic in $a$ for each $c\in(-1/3,0)$. This extends and/or refines certain previously established results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
