Double-triangular Distribution

Double-triangular Distribution is the combination of two triangles, each with an area of 0.5. The mode is also the median.

The mean is:

The variance is:

Note: the variance is the same as for the triangular distribution.

The probability density is:

And the cumulative distribution function:

 

For Monte Carlo simulation random values from the DT can be generated using random numbers between 0 and 1 (here denoted as “p”) and the following formulas:

The double-triangular is quite unnatural. It is highly unlikely to be a proper representation of uncertainty. Moreover, estimating the median is, in my view, more difficult than the estimating the most likely value (mode).