Fitting Beta Distributions Based on Sample Data

Abstract

Construction operations are subject to a wide variety of fluctuations and interruptions. Varying weather conditions, learning development on repetitive operations, equipment breakdowns, management interference, and other external factors may impact the production process in construction. As a result of such interferences, the behavior of construction processes becomes subject to random variations. This necessitates modeling construction operations as random processes during simulation. Random processes in simulation include activity and processing times, arrival processes (e.g. weather patterns) and disruptions. In the context of construction simulation studies, modeling a random input process is usually performed by selecting and fitting a sufficiently flexible probability distribution to that process based on sample data. To fit a generalized beta distribution in this context, a computer program founded upon several fast, robust numerical procedures based on a number of statistical‐estimation methods is presented. In particular, the following methods were derived and implemented: moment matching, maximum likelihood, and least‐square minimization. It was found that the least‐square minimization method provided better quality fits in general, compared to the other two approaches. The adopted fitting procedures have been implemented in BetaFit, an interactive, microcomputer‐based software package, which is in the public domain. The operation of BetaFit is discussed, and some applications of this package to the simulation of construction projects are presented.