I'm working on a cost estimate for a project. I have six categories for the cost estimate. Of the six categories, I know exactly what the cost will be for three of them (50% certain on categories). Based on my best judgement, I have estimates for what the other category costs will be. Based on the combined cost (the sum of the exact cost categories and the estimated cost categories), I have a total estimated cost. In this case, the exact cost estimate accounts for 80% of the total estimated cost. That is, the estimated cost just so happened to be equivalent to a third of the known cost.
I would like to know if there is a way to extrapolate a certainty or error for the combined cost estimate based on the quantity of known data relative to the quantity of estimated data. In this case, it would be based on a 50% certainty for category cost (either certain or uncertain) and 80% certainty for combined cost (percentage of estimated cost to total estimated cost). The problem being the 80% certainty is not exact since it's derived from an estimate and could change based on the proportion of the estimated category costs relative to the known category costs.
My instinct is to multiply the two percentages to get a 40% certainty, but I don't know if this is valid or if there's a rule, like the pareto principle, that could be employed to find a suitable answer. Any insight on this topic would be much appreciated. Thanks
Edit - Here's a reference to the pareto distribution: https://en.wikipedia.org/wiki/Pareto_distribution#Statistical_inference Perhaps the data could be modeled against a particular distribution to realize an error?