CDF-Intervals Revisited

The concept of cdf-intervals introduced in previous work is revisited with a new domain specification, inference mechanism and implementation. A cdf-interval extends traditional convex intervals over reals with a degree of knowledge attached to the data. Instead of approximating the unknown data distribution with the nearest uniform distribution, leading to a linear cdf curve, we bound the unknown probability distribution thus guaranteeing a full encapsulation of the data and its degree of knowledge with two curves. A cdf-interval is now specified by two triplets denoting the lower and upper bounds slopes of the data distribution. A triplet is composed of the data value, degree of knowledge and respectively lowest and steepest slopes. This idea is embodied as a new solver in the ECLPS system, presented in this paper. Experimental results indicate that the solver brings solution insights, leading to tighter bounds when compared with the previous cdf and the convex data interval solvers.

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