How to use the Custom Distribution in Crystal Ball – The Discrete Uniform Distribution (1 of 5)

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 or go to http://www.crystalball.com/modelassist/index.html.

Introduction

The Custom Distribution in Crystal Ball is arguable the most versatile, but also one of the most difficult distributions to correctly use within Crystal Ball. In fact, using the Custom Distribution, a Crystal Ball software user can construct five different kinds of distributions (see Table below).

* The Discrete Uniform distribution as defined in this tip is a discrete probability distribution in which each of the potential values has the same probability. The Discrete Uniform distribution in Crystal Ball is a special case of this, where the discrete values in the distribution also all have the same probability but can only be integers (also known as a Discrete Uniform Integer distribution).

Each of these five distributions has a different use and application. The way that the Custom distribution “knows” which of the above five to make for you totally depends on the format of your input data ("date entry rules").

The goal of this Risk Tip series is to inform you of the five different distributions that you can construct using the Custom Distribution and their various uses. The five Risk Tips will also provide detailed instructions on how to format your data to construct the five different distributions with the Custom Distribution.

Important Note – Dynamic Referencing

When you use the Custom Distribution, we highly recommend that you use data from your spreadsheet and use “dynamic referencing” with the Custom Distribution, because this allows the user to change data in his/her spreadsheet, which will result in appropriate changes in the distributions. You need to take the following steps to use “dynamic referencing” (M0517):

Step 2.
After clicking the "Load Data..." button click the option "Keep linked to spreadsheet" as shown below.

Step 3.
After clicking the option "Keep linked to spreadsheet," select the date on your spreadsheet you like to use. As mentioned above, the data and data format requirement for the Custom will be described in this and the next four Risk Tips.

1. The Discrete Uniform distribution.

The Discrete Uniform distribution is often used for:

1. Bootstrapping your raw data;
2. Fitting empirical distribution to data;
3. Simulating variables that are restricted to specific values (e.g., investment amounts in round $1000; and
4. Used as an Index or Look-up variable in a spreadsheet function.

For more information about application of the Discrete Uniform distribution, see ModelAssist topic M0133.

The Discrete Uniform distribution randomly picks any one of the values you give it with equal probability (sampling with replacement). There are three methods to format your data so that the Custom Distribution "knows" that it has to behave like a Discrete Uniform distribution as is shown below (M0515).

Method 1

The first method is to have all the data in one column, from which the Custom Distribution then randomly picks one value at a time. The data in the figure below is in the column D11:D14, which resulted in the Discrete distribution shown below.

Method 2

Method 3

The third method is more complicated, but is more efficient for setting up a Uniform Discrete distribution with equal distances between the numbers. You have to use exactly four cells, as shown in the figure below. The first cell is the first value of the distribution, and the second cell the last value. The third cell can have any value as long as it is not an empty cell (in our example a "1" is used), and the fourth cell gives the step-size between the different data points as shown below.

What’s Next?

If you like to know more about the Custom Distribution (or about Quantitative Risk Analysis in general), download the free demo of ModelAssist for Crystal Ball. This comprehensive risk analysis reference and training tool will help you perform accurate risk analyses with the Crystal Ball software.

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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, which gives a more detailed explanation of the above methods and any risk analysis techniques involved.