Extended Triangular Distribution
The extended triangular distribution is typically used with cost data in base+contingency mode where there is both quantity uncertainty and a moderate amount of scope uncertainty. Allowance is made for overrunning the contingency limit, but, unlike the lognormal distribution, there is a hard limit to the amount of overrun allowed.
(In Monte Carlo analysis, a lognormal distribution can occasionally generate very high cost values, thus simulating a 'rogue' task whose cost is an order of magnitude or more higher than the estimated cost. The extended triangular distribution does not permit such high costs.)
The extended triangular distribution assumes there is no possibility of any costs below the base estimate. Consequently, the low limit and the base estimate are the same: