I am trying to work on a process to improve how how well my team estimates. I want to look at using some statistics to help out and embrace the uncertainty in how we estimate tasks.
If I have a group of experts and I ask them for a best (b), average (a) and worst (w) case estimate for a task, creating a triangular distribution.
Using a monte carlo method I can generate 10,000 trials using the triangular distribution for each of the estimators and combine these together into one sample set.
I can then use a MLE to create a beta distribution from the sample statistics, then use the cdf(x) functions to determine the likelihood of an estimated number of days, or use the inverseF to determine the number of days to maintain a certain likelihood.
This seems to make sense to me logically, however I am unsure about the fitting of a Beta distribution to the samples. I am wondering if there is a better distribution I should be using, especially given that the samples are just randomly generated from N triangular distributions.
Does anybody have any suggestions or experience in doing this that could point me in the right direction? It's been a few years since I left uni, so my statistics is a little rusty. There are plenty of examples of this process for one expert, however I would like to be able to do the same thing for multiple experts.