  We review the methods of constructing confidence intervals that account for a
priori information about one-sided constraints on the parameter being
estimated. We show that the so-called method of sensitivity limit yields a
correct solution of the problem. Derived are the solutions for the cases of a
continuous distribution with non-negative estimated parameter and a discrete
distribution, specifically a Poisson process with background. For both cases,
the best upper limit is constructed that accounts for the a priori information.
A table is provided with the confidence intervals for the parameter of Poisson
distribution that correctly accounts for the information on the known value of
the background along with the software for calculating the confidence intervals
for any confidence levels and magnitudes of the background (the software is
freely available for download via Internet).
