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...
