 Risk Analysis Tip (a topic drawn from ModelAssist)
Estimating a probability, fraction or prevalence ('p')* Risk analysis modeling often requires the estimation of the uncertainty distribution of a probability, fraction or prevalence from historical data. For example, in marketing we often like to know the market share of a product, in insurance we need to estimate the probability of a house burning down during the next year, or in epidemiology we like to estimate the prevalence of a certain disease.
There are several ways to estimating this probability, fraction or prevalence 'p' from historical data: using classical statistics, the Bootstrap or Bayesian methods, all described in ModelAssist (M0162). Classical statistics offers several ways of estimating the uncertainty distribution of 'p' (M0160), and below we will show you the best (M0111).
Example
Let's assume you need to know the Market Share in a certain geographical area of a shampoo your company sells. You called 23 random people (living in this area) of which 5 said they use our shampoo. What is the uncertainty distribution of our Market Share and how can we model this uncertainty with @RISK or Crystal Ball?
Best Classical Statistics method
This classical statistics method first requires us to construct a cumulative uncertainty distribution, using Excel functions. The following formula represents the confidence we have that the true Market Share is less than any specific tested value 'p':
=1-BINOMDIST(s,n,p,1)+0.5*BINOMDIST(s,n,p,0)
=1-BINOMDIST(5,23,p,1)+0.5*BINOMDIST(5,23,p,0)
which will result in the following cumulative distribution:
In your @RISK or Crystal Ball model, you can then use the above cumulative distribution to model the uncertainty about the Market Share of your shampoo, using a Cumulative Distribution.
A special situation arises when the number of success s (in this example that would be the number of people you called that said they use your Shampoo) is zero. In that situation, there are two possibilities; (1) you know for sure that people use your Shampoo in this geographic area and thus Market Share is for sure > 0 or (2) you do not know for sure people actually use your Shampoo in this geographic area. In the latter situation, the uncertainty distribution assigns 50% confidence to p = 0, and the remaining 50% confidence to all other Market Share values. The Bayesian equivalent of this would be to assign a prior distribution with 1/3 confidence assigned to p=0 and p=1 each, and 1/3 confidence distributed over p = 0 to p = 1.
This method of estimating the uncertainty distribution of a probability, fraction or prevalence is also available in an Excel spreadsheet model for  @RISK, Crystal Ball 5.5- or Crystal Ball 7.0+ users.
- The material within this 'Risk Analysis Tip' comes from one of the hundreds of topics available in ModelAssist. ModelAssist gives a more detailed explanation of the above methods and any risk analysis techniques involved.
- (M0162), etc. are ModelAssist topic references. To find the appropriate page simply type the code in the Search dialogue box.
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