Choosing A Distribution
Full Monte, Barbecana’s new risk analysis software and Microsoft Project add-in, supports five different families of distribution: normal, lognormal, beta, triangular, and uniform. Other project management tools support more, but even with five, the choice is likely to be daunting for many users. The fact is that it doesn’t matter that much. As Sam Savage says in his recent book (The Flaw of Averages), “In the land of averages the man with the wrong distribution is King.” Nevertheless, some guidance might be in order.
Normal Distribution
Many natural stochastic processes seem to result in the Normal distribution, which is perhaps where it gets its name. One explanation for this is the Central Limit Theorem, which says that if you add a number of independent random variables together, regardless of what individual distributions they are drawn from (as long as each has a finite mean and standard deviation), the distribution of the sum will tend towards the normal distribution. So, to the extent that a task could be regarded as a succession of smaller tasks, it would not be surprising if the distribution of task duration were normal.
One problem with the normal distribution, however, is that it is symmetrical. It also has infinitely long tails, so by definition any normal distribution includes a finite possibility of negative values. A negative task duration is not easily interpreted and generally not allowed. (This may seem like it contradicts the central limit theorem but it doesn’t; as the number of random variables added together increases, the mean increases faster than the standard deviation, and the distribution tends towards normal. At the infinite limit the size of the negative tail tends to zero.) For the purposes of Full Monte, it is assumed that the user-defined optimistic and pessimistic values represent a six–sigma range and the sampling method suppresses values outside that range.
Continue reading about our Microsoft Project add-in, Full Monte, and the distributions it supports -
