Choosing among different discrete approximations of a continuous random variable

For many complex probabilistic problems involving continuous random variables, it is impossible to find a closed-form solution. Consequently, it is necessary to approximate a given continuous probability distribution with a discrete one. Several techniques are available for producing a discrete approximation to a continuous random variable, based on rather di↵erent criteria. In this work, we will examine and compare these main methods, by considering a well-known parametric distribution. Applications to real problems will finally be suggested.