Various Uses of Distributions in Risk Analysis (2 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 Risk Analysis Tip, we discussed that the correct design and development of Crystal Ball models is highly dependant on the risk analyst’s understanding of the exact use (meaning) of the distributions (Crystal Ball assumptions) he or she uses. We also introduced and explained the three different conceptual uses of distributions and gave a short introduction to "Uncertainty Distributions." In this Risk Analysis Tip, we provide you with an explanation of Frequency Distributions.

Frequency Distributions

A frequency distribution describes the variability of individuals in a sample from a population. This type of distribution is therefore also sometimes called a distribution of "inter-individual variability." For example, we may have collected income data of people in a certain area of the country or about the size of individual loans of a bank’s clients. Individuals in the latter example are therefore obviously the loans (i.e. individuals of course don’t have to be people).

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

Finance example: Imagine you are a bank and have say 5,000 outstanding loans. Each of these loans has certain probably of default within a certain time period (such probably can for example be represented by a Beta distribution as explained here. How can you model such situation?

First, you can represent the "inter-individual variability" of the different loans sizes (just the raw data you have, see Table to the right) with a frequency distribution. There are a number of ways to do this, including for creating a histogram of the observed data (gray bars on figure below) or fitting a distribution to the data using Crystal Ball’s distribution fitting feature.

When we fit a distribution to our loan size data using (in this example we use ‘fake’ data), Crystal Ball checks for the fit of a number of continuous distributions as show in the Figure below. In this example the Lognormal distribution fits the best according to the Anderson Darling (AD) statistic (click here to see some considerations for distribution fitting).

Let’s assume that a Lognormal distribution for loan sizes makes sense, then this fitted distribution represents the inter-individual variability of loan sizes for this bank. The distribution truly has no random components in it; it just is an alternative representation of the data (instead of a table, a graph).

Now, when we actually use this distribution in Crystal Ball to, for example, calculate how much default losses we may have during the next year, this "frequency distribution" turns into a "probability distribution" or a distribution of randomness. Probability or randomness distributions, the third category of the conceptual use of distributions, are however the topic of our next and final Risk Analysis in this short series.

Conclusion

Frequency distribution represents the inter-individual variability of a certain variable, such as for example loan size. There are no random components in a frequency distribution. When we ‘randomly’ start drawing observations from a frequency distribution (i.e. using that distribution in a Crystal Ball “assumption”), the frequency distribution turns into a probability or randomness distribution, which will be discuss in more detail in our next Risk Analysis Tip.

What’s next?

If you like to know more about how to present your Crystal Ball results using Graphical or Statistical descriptions, ModelAssist for Crystal Ball gives you a more complete list of good practices on how to present your Crystal Ball model and its results.

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* 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.