## Simulation of non-uniform distributed random variables

So far, the simulation of the same random variable was discussed. In fact, the generation of uniform random numbers is a very important step. The methods for generating non-uniform random numbers are different. The main aim is to transform random numbers from a uniform distribution to another distribution. Generally, a uniformly distributed random variable, can accordingly be transformed and modified to obtain other distributions.

### The inversion method

The condition is that uniformly distributed random numbers are already generated in the interval [0,1]. The inversion method takes advantage of the fact that a distribution function is also defined in the interval [0,1].

Let be the distribution function of V. Through the plug-in of a uniform random number into the inverse distribution function

, we get a random number with the distribution V.

A prerequisite for the application of an inversion process is therefore the existence of the analytic...