CHAPTER 9 The Selection of Distributions for Use in Risk Models

This chapter describes key distributions that are required to capture the uncertainty profile of input variables in risk models. We describe their occurrence, some of their practical uses, methods to approximate one with another, as well as the topic of distribution selection.

Chapter 10 covers the specific calculation processes required to create random (percentile-value) samples from these distributions using inversion of their cumulative distribution functions, a process that is essential for those wishing to implement risk modelling using Excel/VBA. Chapter 11 covers the creation of relationships that involve dependency between distribution samples, which is relevant for users of both Excel/VBA and @RISK.

In this chapter, we describe over 20 distributions. These are generally sufficient for the large majority of practical applications in business risk modelling, and all are available in both Excel/VBA and @RISK (which also has more). Much of the subject can be adequately understood by focusing on their visual and basic statistical properties. However, some mathematics is necessary in places, in particular to be able to compare and approximate distributions, and to create inverse cumulative distribution functions when using Excel/VBA approaches.

The graphical displays in this chapter use both Excel and @RISK, and some results of simulations are shown. Most (but not all) of the calculations used to produce the ...

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