Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution

This paper introduces a new probability distribution referred to as a transformed triangular distribution (TTD) by using the average of the extreme values (minimum and maximum) of the triangular distribution. The TTD is being approximated by the continuous uniform distribution. The basic moments of the TTD and those of the continuous uniform distribution are compared respectively, and a relationship established. This can be used in modeling and simulation.