The triangular distribution is a useful tool if a variable has to be estimated subjectively. The estimator has to indicate a **Low**, a **Most Likely value (Mode)** and a **High** value, the distribution contained within the Low to High range. In the formulas below "** l**" is the Low, "

The mean is:

The variance is:

The CDF consists of two curved line segments, with a discontinuity at the mode.

In this case it is interesting to know also the inverse form of the cumulative distribution function:

This formula is used in generating a random triangular deviate from a rectangular one between 0 and 1 in Monte Carlo analysis.