Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Obtaining a Trapezoidal Distribution



James F. Lawrence, Raghu N. Kacker, Ruediger Kessel


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.
Communications in Statistics Part A-Theory and Methods


Kullback-Leibler uniform deviation, Measurement uncertainty, Sinkhorn balancing, Trapezoidal distribution


Lawrence, J. , Kacker, R. and Kessel, R. (2015), Obtaining a Trapezoidal Distribution, Communications in Statistics Part A-Theory and Methods, [online], (Accessed February 24, 2024)
Created March 9, 2015, Updated March 12, 2019