Distributions and correlations in Monte Carlo simulation

The use of Monte Carlo simulation in construction cost analysis is of interest to construction professionals as part of the risk analysis of construction projects. In recent high profile publications the presentation of Monte Carlo simulation based cost analysis overplays the importance of the choice of which distribution to use to represent input variables and underplays the importance of assessing and including correlations between the variables. The British literature also overplays the suitability of the beta distribution to represent input variables. This paper addresses these issues using a data set comprising elemental rates from 216 office buildings drawn from the BCIS of the RICS. Using a chi-squared test for goodness of fit it is shown that lognormal distributions are superior to beta distributions in representing the data set. Simulation runs of the cost model including and excluding correlations show that correlations must be included in Monte Carlo simulation otherwise the analysis leads to serious misassessment of risk. Simulation results show also that the effect of excluding correlations is more profound than the effect of the choice between lognormal and beta distributions.