Summation of lognormal distributed random variables

In the above image, you can see how a lognormal distribution is convolved with itself ten times, which corresponds to the addition of the underlying random variables. The resulting distribution has been scaled by the number of convolutions in each case, so you can see how the shape of the distribution changes.

Immediately notice how the resulting distribution gets narrower at each step. This is the central limit theorem of probability theory, which states, among other things, that under various conditions the distribution function of summed random variables becomes narrower and narrower.

For us, the most important of these conditions is independence, i.e. that the various estimation elements must not influence each other. For project management, this is certainly wrong, since each estimated package, if it takes longer, for example, will increase the total duration of the project and thus increase the effort required to manage the project. This general problem can be addressed by estimating such dependent packages (e.g., system testing and bug fixing) only at the end, when the effort for the whole rest of the project is already known.