关于分布函数的反函数的一些结果

Some Findings on the Inverse Function of Distribution Function

随机变量的分布函数及其反函数在概率论中占有重要地位.由于分布函数一般不是严格单调的,研究其反函数就遇到了一定困难.本文给出了分布函数的反函数的定义,并证明了其合理性.运用分析理论中的确界原理等方法证明了反函数的几个重要性质,并讨论了其在随机变量的存在性、分位数、随机模拟等方面的重要应用.

Random variable distribution functions and their inverse functions take an important role in probability theory. Generally, distribution functions are not strictly monotonous; this makes it difficult to study their inverse functions. After defining the inverse functions of distribution functions, the authors have proved the rationality of inverse functions, identified some of the important properties of inverse functions by using least bound theory, and made an discussion on their applications in the existence, quantile, and random simulation of random variables.