Various Uses of Distributions in Risk Analysis (3 of 3)

The following Risk Analysis Tip is provided by Dr. H. Groenendaal (Huybert@risk-modeling.com) at Vose Consulting, and has been drawn from material in ModelAssist® for Crystal Ball®, the comprehensive risk analysis training, reference and template software. ModelAssist users can consult the ModelAssist-references (in the form of Mxxx) for additional information. To read more about ModelAssist and get a free download of the demo version, click here.

Introduction

In the previous two Risk Analysis Tips (Various Uses of Distributions, Part 1 and Various Uses of Distributions, Part 2), we discussed how the correct design and development of probabilistic models (with Crystal Ball software) is highly dependent on the risk analyst’s understanding of the exact use (meaning) of the distributions (Crystal Ball assumptions) that he or she uses. We introduced and explained the three different conceptual uses of distributions and gave an introduction to Uncertainty Distributions (Part 1) and Frequency Distributions (Part 2).

In today’s Risk Analysis Tip, we provide you with an explanation of Probability Distributions. It’s highly recommended that (if you have not done so yet), you read the previous two tips first.

Probability Distributions

A probability distribution describes the values of a random variable. This type of distribution is therefore also sometimes called a distribution of randomness. For example, we may want to simulate a poker game or the number of credit loss events a bank will have during the next year. In both situations, we would use probability distributions to model the randomness.

There are two types of "distributions of randomness." The first is when we take random samples from a frequency distribution. The second is when we model a random process such as a binomial process (see Risk Tip #6 for more information about the Binomial Process).

To help you better understand how to think about frequency distributions, imagine the following example.

Finance example: Let’s take the same problem as we did in our last Risk Tip. As stated in that tip, if we take random samples from a Frequency distribution (in this case, from a distribution of individual loan sizes), the distribution now becomes a Probability distribution.

Sales person example: A second example considers a sales person placing calls to customers. On a typical day, the sales person can place about 200 calls, and each call has about a 8% probability of selling one product. How many products will the sales person sell tomorrow?

The answer to this questions is a binomial distribution with n = 200 and p = 8%, as is shown in the figure below (again, see Risk Tip #6 for more information).

This is an example of a probability distribution, i.e. a distribution that describes randomness.

Conclusion

A Probability distribution represents a random variable, used in circumstances such as for picking random individual loan size or placing sales calls.

What’s next?

If you like to know more about Frequency, Uncertainty and Randomness distributions (and their relationships and possible mixture), ModelAssist for Crystal Ball gives you a more complete list of good practices on how to present your Crystal Ball model and its results.

> Learn more about ModelAssist for Crystal Ball and download a demo version today

* The material within this ‘Risk Analysis Tip’ comes from one of the over 500 risk analysis topics available in ModelAssist for Crystal Ball. ModelAssist for Crystal Ball gives a more detailed explanation of the above methods and any risk analysis techniques involved.