Automatically Verified Arithmetic on Probability Distributions and Intervals
Representing and operating on operands which are probability distribution functions; and
Representing and operating on operands when one is a distribution function and the other is an interval.
We discuss how to do these operations and get automatically verified results, using a method based on histograms. Histograms are composed of bars, each with an associated interval and probability mass. A histogram discretizes a probability distribution function in that each bar represents a portion of it, with the area of the bar equal to the area of the distribution function over that part of its domain corresponding to the interval-valued portion of the x-axis under the bar.
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