Generating a Random Sample from discrete probability distribution

If is a discrete random variable taking on values ， then we can write

.

Implementation of this formula to generate discrete random variables is actually quite straightforward and can be summarized as follows.

To generate ,

1. Generate
2. if , set .

we define and .

算法来源：Statistical Inference (统计推断，英文版，原书第2版)，Chapter5.