Plotting data is one guide to selecting a probability distribution. The following steps provide another process for selecting probability distributions that best describe the uncertain variables in the spreadsheets.
To select the correct probability distribution:
Look at the variable in question. List everything you know about the conditions surrounding this variable.
You may be able to gather valuable information about the uncertain variable from historical data. If historical data are not available, use judgment, based on experience, to list everything you know about the uncertain variable.
For example, look at the variable “patients cured” that is discussed in Tutorial 2 — Vision Research. The company plans to test 100 patients. You know that the patients will either be cured or not cured. And, you know that the drug has shown a cure rate of around 0.25 (25%). These facts are the conditions surrounding the variable.
Review the descriptions of the probability distributions.
Probability Distribution Descriptions describes each distribution in detail, outlining the conditions underlying the distribution and providing real-world examples of each distribution type. As you review the descriptions, look for a distribution that features the conditions you have listed for this variable.
Select the distribution that characterizes this variable.
A distribution characterizes a variable when the conditions of the distribution match those of the variable.
The conditions of the variable describe the values for the parameters of the distribution in Crystal Ball. Each distribution type has its own set of parameters, which are explained in the following descriptions.
For example, look at the conditions of the binomial distribution, as described in Binomial Distribution:
For each trial, only two outcomes are possible: success or failure.
The trials are independent. What happens on the first trial does not affect the second trial, and so on.
The probability of success remains the same from trial to trial.
Now compare the “patients cured” variable in Tutorial 2 — Vision Research with the conditions of the binomial distribution:
Two possible outcomes exist: the patient is either cured or not cured.
The trials (100) are independent of each other. What happens to the first patient does not affect the second patient.
The probability of curing a patient 0.25 (25%) remains the same each time a patient is tested.
Since the conditions of the variable match the conditions of the binomial distribution, the binomial distribution would be the correct distribution type for the variable in question.
If historical data are available, use distribution fitting to select the distribution that best describes the data.
Crystal Ball can automatically select the probability distribution that most closely approximates the data’s distribution. The feature is described in detail in Fitting Distributions to Historical Data. You can also populate a custom distribution with the historical data.
After you select a distribution type, determine the parameter values for the distribution. Each distribution type has its own set of parameters. For example, the binomial distribution has two parameters: trials and probability. The conditions of a variable contain the values for the parameters. In the example used, the conditions show 100 trials and 0.25 (25%) probability of success.
In addition to the standard parameter set, each continuous distribution (except uniform) also lets you select from alternate parameter sets, which substitute percentiles for one or more of the standard parameters. For more information on alternate parameters, see Using Alternate Parameter Sets. For a summary list of parameters for each probability distribution, see the Oracle Crystal Ball Reference and Examples Guide.