Random phenomena are clearly of various kinds, and their probabilistic description makes use of numerous probability laws. In this chapter, we present the most important, and most commonly used of these laws, giving their main characteristics (distribution function, transforms, moments) and commenting the "circumstances" under which they are likely to appear.

The specialist is to apply these laws in various situations. For instance, an experimental distribution of a character has been obtained in a measurement campaign, and the goal is to build a theoretical model able to represent the result. This amounts to adjusting a mathematical model using the measurements. Another case is in the choice a priori of the model of a process in an ongoing project (typically for a simulation experiment). Here, the choice of law is made by invoking intuitive or mathematical arguments sustaining a specific law. Needless to say, such a choice relies mainly on the specialist's experience. Lastly, the need occurs to analyze the behaviour of a phenomenon of given probability distribution (e.g. obtained through one of the previous steps). The analysis is based upon the properties of the law (moments, transforms) and makes it possible to draw various figures of interest (e.g. loss probabilities, average delays, etc.).

Depending on circumstances, observations are represented using discrete laws (number of events arriving in an observation window, number of failures, etc.) or continuous ones (e.g. service duration). Denoting the random variable as X, the law is thus either discrete, defined by a...