In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower right-tail bounds depend only on the probability density function (PDF), its first derivative, and two parameters that are used for tightening the bounds. These tail bounds hold under certain conditions that depend on the PDF, its first and second derivatives, and the two parameters. The new tail bounds are shown to be tight for a wide range of continuous random variables via numerical examples.

翻译：本文提出了一种全新的连续随机变量右尾概率上下界，适用于无界支撑和左半有界支撑的连续随机变量。所提出的右尾上下界仅依赖于概率密度函数（PDF）、其一阶导数以及两个用于收紧边界的参数。这些尾部边界在特定条件下成立，该条件取决于概率密度函数、其一阶和二阶导数以及这两个参数。通过数值示例表明，新尾部边界对广泛的连续随机变量具有紧致性。