# Combining two triangular distributions to yield one distribution

I am interested in using some Monte Carlo methods to help with an estimation problem I have. I need to allow multiple estimators to estimate line-items giving a best, average and worst case estimate (standard 3-point estimating). That is I can have 2 or more people giving 3 values for a particular item.

What I need is a mechanism for combining these estimate values (triangular distributions) together to create one unified distribution that I can then use for sampling values from for the Monte Carlo trials.

Is what I am asking even possible, or am I approaching this the wrong way?

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You can certainly make each person's triangular distribution into a pdf. Then the group pdf is the rescaled product of these. If one person's worst is greater than another's best you are sunk. One approach would be to make everyone's estimate into a bell-shaped pdf with best and worst being $3\sigma$ (with something done if they are not symmetric around the average). Then you can multiply them and rescale to get the consensus pdf. In the case people disagree as above, it will depend sensitively on how broad the tails of the distribution you choose are. One good test is what happens to your blending if I say "it will certainly be $1$". This will spoil many reasonable-sounding plans.