Applications of Interval Computations pp 227-244 | Cite as

# Automatically Verified Arithmetic on Probability Distributions and Intervals

## Abstract

- 1.
Representing and operating on operands which are probability distribution functions; and

- 2.
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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