# Modelling uncertainty with probability distributions

Suppose we’re building a system with certain qualities that we’re interested in, e.g. response time, battery usage, etc. Each of the system’s qualities depends on our decision about components we use to build the system. We only know how the decisions impact the qualities of our system with uncertainty, e.g. deciding to use a GPS module will most likely add an extra 10µJ to our battery usage, but could add anything between 9-14µJ. Is it common to model this uncertainty using probability distributions? Is beta distribution a good choice here? Or would triangular or uniform distribution be more sensible in this case? In case of beta distribution, how do I work out the α and β parameters knowing the most likely and limiting estimates only?

Note: my knowledge in statistics is rather limited.

## 1 Answer

I find it difficult to work out here if this is an abstract model or something that will be applied to real data.

The beta, triangle and uniform distributions (the last a special case of the first) are all best used only when there are absolute limits on what is possible, e.g. all values must be within (0,1). It sounds as if 9 and 14 $\mu$J are likely or plausible limits only. You'd be better off using a distribution with infinite limits, such as a Gaussian, surprising though that may seem.

• Thanks for your answer and language check, Nick. This will be applied to real data where the decision impacts on system qualities will be domain expert guestimates in the form of most likely and (as you noted correctly) plausible limits. If I should use a Gaussian as you suggested, how do I compute the parameters here? Clearly, the distribution will be skewed in most cases. Thanks! Jun 7 '13 at 10:30
• That was not clear to me from your posting, but if you know that a distribution is skewed something like a gamma distribution might make more sense. If your domain experts really are experts, why are not they doing the guessing? More seriously, there is literature on how to quantify uncertain information, but it's way outside my field and you should hope for better answers from others. Jun 7 '13 at 10:40