论文标题
伽玛分布家族的单调性能
Monotonicity properties of the gamma family of distributions
论文作者
论文摘要
对于真实$ a> 0 $，令$ x_a $表示带有参数$ a $和$ 1 $的伽马分布的随机变量。然后，$ \ mathsf P（x_a-a> c）$在每个实际$ c \ ge0 $中增加$ a $;每个实际$ c \ le-1/3 $ in $ a $ in $ a $;每个$ c \ in（-1/3,0）$中的$ a $中的非单调。这扩展和/或完善了某些先前确定的结果。
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.
