  This paper introduces a new constraint domain for reasoning about data with
uncertainty. It extends convex modeling with the notion of p-box to gain
additional quantifiable information on the data whereabouts. Unlike existing
approaches, the p-box envelops an unknown probability instead of approximating
its representation. The p-box bounds are uniform cumulative distribution
functions (cdf) in order to employ linear computations in the probabilistic
domain. The reasoning by means of p-box cdf-intervals is an interval
computation which is exerted on the real domain then it is projected onto the
cdf domain. This operation conveys additional knowledge represented by the
obtained probabilistic bounds. The empirical evaluation of our implementation
shows that, with minimal overhead, the output solution set realizes a full
enclosure of the data along with tighter bounds on its probabilistic
distributions.
