Obtaining a Trapezoidal Distribution

Abstract

Given a most believed value for a quantity together with upper and lower possible deviations from that value, a rectangular distribution might be used to represent state-of-knowledge about the quantity. If the deviations are themselves known by probability distributions, and the value conditioned on the deviations is rectangular, then the marginal distribution of the value is determined by the distributions of the deviations. Here we show under quite general conditions that conversely, given the marginal distribution, the distributions of the deviations are uniquely determined. The case in which the marginal distribution is trapezoidal is studied in some detail.

Keywords:

• Kullback-Leibler uniform deviation
• Measurement uncertainty
• Sinkhorn balancing
• Trapezoidal distribution.

Mathematics Subject Classification:

• primary, 60E05, and 62E17