Defining triangular probability distributions from historical cost data

During the development of an automated cost estimating system, several factors led to the selection of the triangular probability-density function to model historical construction costs. The triangular-density function is customarily used when function parameters are directly estimated by experts. A typical example is for estimating activity durations by identifying a minimum value, a most likely value, and a maximum value. These values are then used to construct triangular-density functions to represent uncertain activity durations. For this work, however, it was necessary to estimate parameters of the triangular-density function using historical cost data. A methodology was developed to generate test data and compare three methods of parameter estimation - maximum likelihood, moment matching, and least-squares curve-fitting techniques. It is concluded that optimized moment matching and least-squares techniques produce more accurate parameter estimates, while maximum likelihood estimation yields less accurate results. It is further concluded that the least-squares minimization method always performed as well as or better than the optimized moment matching technique and was therefore selected as the method of choice for the project.