The triangular distribution is popular in risk analysis because it seems to naturally embody the idea of ‘three point estimation’, where subjective judgement is used to estimate a minimum, a ‘best guess’ and a maximum value of a variable such as the cost of an item or the time taken to accomplish a task. It looks mathematically simpler than many of the standard distributions and could be regarded as the simplest probability density function that embodies a random variable with a given minimum, mode and maximum. Because of this, you may be tempted to think of it as the distribution that involves fewest assumptions and that it is therefore the one to use when you don’t know what the real distribution is. Its Wikipedia article says ‘… the triangle distribution has been called a “lack of knowledge” distribution’. Although the article gives no reference for this assertion, and I’ve never seen it explicitly stated anywhere else, it sounds plausible and I do think it represents the main reason people use the triangular distribution.

The problem with this idea is that it isn’t true. Read more