How to generate almost random numbers

Sammanfattning

In this thesis we will explore methods to generate random numbers from any distribution. The basic idea behind generating random numbers is to use a mathematical sequence for which it should be impossible to guess what the next number is without knowing exactly how the sequence is generated. Although any hard to guess sequence would work, this thesis focuses on the linear congruential sequence, $X_{n+1}=aX_n+c\mod m$. There are two advantages to this sequence, firstly it is quick, secondly it has underlying theorems on how to use it. These theorems which have been studied in Donald Knuths the Art of Computer Programming volume 2, will be explored and proven in this paper. To get any distribution we will also need the inversion and rejection methods. The effectiveness of these as methods to get random numbers is what W.Hörmann and G.Derflinger has studied in their paper. We will do the same testing of those methods and try to replicate their results. Replicating their results failed, however the same conclusion can be drawn.