Useful elements in common between gH-based extended-interval and probabilistic arithmetic

Building on new properties of generalized Hukuhara (gH) operations - in particular, the fact that gH-based arithmetic identifies the exact core (i.e., the points of maximum PDF value) of variable Z = XoY when X, Y are uniform random variables on compact intervals and o is one of the four arithmetic operations - we show that, when combined with the well-known property that Minkowski-based arithmetic provides the exact support of Z, the PDF of Z, in the family of generalized trapezoidal distributions, can be accurately approximated by linearly connecting the extremes of its support and core. This result enables a new, efficient implementation of histogram-based arithmetic for general random variables X, Y whether independent or dependent.