Lognormal Distribution
Full Monte is a schedule risk analysis tool that operates seamlessly as a Microsoft Project add-in. While Full Monte supports normal distributions, it is often the case that people think an asymmetrical distribution is more representative of reality. In particular, they think it is more likely that the actual duration will exceed the expected value by a large amount than that it will fall short of it by the same amount. To take an extreme example, if things go badly wrong a task could take twice as long as expected, whereas there is no chance that it will take no time at all. One convenient asymmetric distribution is the lognormal distribution.
The lognormal distribution is the distribution of a variable whose logarithm is distributed normally. Since the log of zero is minus infinity – or more properly the log(x) tends to minus infinity as x tends to zero – this means that the left-hand tail of the distribution has a definite end point at zero. So, the duration cannot be negative and that’s a good thing. The right hand tail is still infinite, however. In Full Monte, the user specifies two values defining a six-sigma range, and the whole shape of the distribution is determined by the ratio of these two values. (If the ratio is small, the lognormal looks much like the normal distribution.) Dan Trietsch of the American University of Armenia offers some empirical evidence that the lognormal distribution is often appropriate. (See here.)
Several other studies have suggested that the lognormal distribution best represents empirical data on task costs in construction, including:
David Wall, Distributions and correlations in Monte Carlo simulations, Construction Management and Economics, 1997, 15, 241-258.
Touran, A. and Wiser, E.P. (1992) Monte Carlo technique with correlated random variables. Journal of Construction Engineering and Management, 118(2), 258± 272.
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