Truncated Gaussians as Tolerance Sets

Abstract

This work focuses on the use of truncated Gaussian distributions as models for bounded data-measurements that are constrained to appear between limits. We prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. We present the characteristic function for the truncated Gaussian; from this, we derive algorithms for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of our methods, we describe a derivation of the disparity constraint (used in computer vision) from our models. Our approach complements in Statistics, but our proposal is not only to use the truncated Gaussian as a model for selected data; we propose to model measurements as fundamentally bounded in terms of truncated Gaussians.