A minimum entropy criterion for distribution selection for measurement uncertainty analysis

Abstract

This paper presents a minimum entropy criterion for selecting the best probability distribution among a set of candidate distributions based on available information for measurement uncertainty analysis. We consider two cases that are most commonly encountered in practice: A and B. In Case A, the available information is a series of observations. In Case B, the available information is the maximum permissible error according to manufacturer’s specification. Three candidate distributions are considered in Case A: the scaled and shifted z-distribution (i.e. normal distribution), the scaled and shifted t-distribution, and the Laplace distribution. Five candidate distributions are considered in Case B: rectangular, triangular, quadratic, raised cosine, and half-cosine. According to the proposed minimum entropy criterion, the scaled and shifted z-distribution is the best distribution in Case A, and the raised cosine distribution is the best distribution in Case B. A case study is presented to demonstrate the effectiveness of the proposed minimum entropy criterion.