The Cumulative Ascending Distribution (Tip #5 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.decisioneering.com/modelassist/index.html.
Introduction
The Custom Distribution in Crystal Ball is one of 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 user can construct five different kinds of distributions (see Table below).
Risk Analysis Tip |
Distribution |
Name used in Crystal Ball Manual |
Tip 1 of 5 |
1. Discrete Uniform distribution |
"Unweighted values" |
Tip 2 of 5 |
2. Discrete distribution |
"Weighted values" |
Tip 3 of 5 |
3. General distribution |
"Sloping continuous ranges" |
Tip 4 of 5 |
4. Histogram distribution |
"Continuous ranges" |
Tip 5 of 5 |
5. Cumulative Ascending distribution |
"Sloping continuous cumulative ranges" |
Each of these five distributions have different uses and applications. 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 (and the last tip and the next three) Risk Analysis tip(s) is to make you aware of the five different distributions that you can construct using the Custom Distribution and their various uses. The five 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 allow the user to change data in his/her spreadsheet, which will result in appropriate changes in the distributions. You can read more about that in the Previous Risk Analysis Tip (Tip 1 of 5) .
1. The Cumulative Ascending distribution.
The Cumulative Ascending distribution is very useful in:
- constructing empirical first and second order empirical distributions of data,
- constructing distributions when using classical statistical methods, and;
- modeling expert opinion.
See more about these applications of the Cumulative Ascending distribution at ModelAssist topic M0109.
To construct a cumulative ascending distribution, the Custom Distribution needs its input in three columns:
- a list of minimum values,
- a list of maximum values and
- a list of cumulative probabilities, F(x), associated with those ranges.
In addition, when you define the assumption, you have to specify that the data are cumulative by clicking the "Probabilities are cumulative" button as shown in the first figure below;
Crystal Ball then constructs a cumulative distribution by straight-line interpolation between the points defined on the curve. Using the data shown above, his will result in the cumulative distribution 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.
ModelAssist
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.
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