Inverse transform sampling反变换采样法

感谢上海交大黄晨博士的博客：https://blog.youkuaiyun.com/doublehhcc/article/details/81166502
亦感谢上海交大博士生许志钦（现为纽约大学克朗研究院博士后）为直观解释所作的贡献，令博主与黄晨同学恍然大悟。

Goal:

Let ${\displaystyle X}$ be a random variable whose distribution can be described by the cumulative distribution function ${\displaystyle F_{X}}$.
We want to generate values of ${\displaystyle X}$ which are distributed according to this distribution.

Algorithm:

The inverse transform sampling method works as follows:

• Generate a random number ${\displaystyle u}$ from the standard uniform distribution in the interval