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Moore and Yang defined an integral notion, based on an extension of Riemannsums, for inclusion monotonic continuous interval functions, where theintegrations limits are real numbers. This integral notion extend the usualintegration of real functions based on Riemann sums. In this paper, we extendthis approach by considering intervals as integration limits instead of realnumbers and we abolish the inclusion monotonicity restriction of the intervalfunctions and this notion is used to determine interval probability densityfunctions.

Interval probability density functions constructed from a generalization of the Moore and Yang integral