The precision of a risk analysis relies very heavily on the appropriate use of probability distributions to accurately represent the uncertainty and variability of the problem. In our experience, inappropriate use of probability distributions has proved to be a very common failure of risk analysis models. It stems, in part, from an inadequate understanding of the theory behind probability distribution functions and, in part, from failing to appreciate the knock-on effects of using inappropriate distributions. This compendium is intended to alleviate the misunderstanding by providing a practical insight into the various types of probability distributions in common use.
This compendium gives a very complete summary of the distributions used in risk analysis, an explanation of where and why they are used, some representative plots and the most useful descriptive formulae from a risk analysis viewpoint. The distributions are given in alphabetical order. The list comprises all the distributions that we have ever used in our consulting work (and have therefore included in ModelRisk), so we are pretty confident that you will find the one you are looking for. Distributions often have several different names depending on the application so if you don’t find the distribution you are searching for here do a search and you may find the alternative name is noted.
Most risk analysis and statistical software offer a wide variety of distributions, so the choice can be bewildering. This compendium therefore starts with a list of different applications, and the distributions that you might find most useful. Then we offer a little guide on how to read the probability equations that feature so prominently in this compendium: people’s eyes tend to glaze over when they see probability equations but with a few simple rules you will be able to rapidly ‘read’ the relevant parts of an equation and ignore the rest, which can give you a much more intuitive feel for a distribution’s behavior.
A compendium of distributions used in modelrisk - whitepaper