Exploring generic methods for random distributions
Most programming languages provide users with functions for the generation of pseudorandom numbers with uniform distributions in the range of [0, 1]. These generators are, very often, considered to be continuous. However, in reality, they are discrete even if they have a very small discretization step. Any sequence of pseudorandom numbers can always be generated from a uniform distribution of random numbers. In the following sections, we will examine some methods that allow us to derive a generic distribution starting from a uniform distribution of random numbers.
The inverse transform sampling method
By having a PRNG with continuous and uniform distributions in the range of [0, 1], it is possible to generate continuous sequences with any probability distribution using the inverse transform sampling technique. Consider a continuous random variable, x, having a probability density function of f(x). The corresponding distribution...
