Defining Triangular Probability Distributions from Historical Cost Data

• Published in: Journal of construction engineering and management Vol. 126; no. 1; pp. 29 - 37
• Main Authors: Back, W. Edward, Boles, Walter W, Fry, Gary T
• Format: Journal Article
• Language: English
• Published: Reston, VA American Society of Civil Engineers 01.01.2000
• Subjects: Applied sciences; Building economics. Cost; Buildings. Public works; Exact sciences and technology; TECHNICAL PAPERS; Construction cost; Case study; Least squares method; Building economy; Probability density function; Cost estimation; Maximum likelihood; Curve fitting; Comparative study; Method study
• ISSN: 0733-9364; 1943-7862
• DOI: 10.1061/(ASCE)0733-9364(2000)126:1(29)

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.