The generalized maximum entropy trapezoidal probability density function. http://dx.doi.org/10.1088/0026-1394/45/4/N01

Abstract

Quantities that lie within inexactly prescribed intervals arise frequently. A formula for the
maximum entropy probability density function (PDF) that describes the state of knowledge of
such a quantity is given in Supplement 1 to the Guide to the Expression of Uncertainty in
Measurement. However, this formula applies only to the case for which the limits of the
interval are known to lie within subintervals of equal lengths centred on the best estimates of
the limits. In this paper, a PDF is derived for a quantity that is not so restricted.