What is advantage of using the theory of point processes instead of probability distribution functions? I am interested in applications of point processes in machine learning, so I have been studying the theory of point process. However, I cannot see advantage of the theory of point processes compared with the classical probability theory. 

For examples, I know the points of a Poisson point process scatters uniformly on a given domain. But, I'm confused what is the difference between Poisson point processes and uniform distribution functions (especially on a bounded domain). 

I have similar questions for not only Poisson point processes but other point processes. Take sample points according to a point process. Can we obtain a similar (random) point set via using a probability distribution function?  

What is advantage of using the theory of point processes instead of using probability distribution functions in statistics and machine learning? 

Thank you so much in advance.
Machine learning is about finding a model for your data and sometime the Point process is a better model than uniform or normal probability distribution.