  For estimating a lower bounded parametric function in the framework of
Marchand and Strawderman (2006), we provide through a unified approach a class
of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist
coverage probability bounded below by $\frac{1-\alpha}{1+\alpha}$. In cases
where the underlying pivotal distribution is symmetric, the findings represent
extensions with respect to the specification of the credible set achieved
through the choice of a {\it spending function}, and include Marchand and
Strawderman's HPD procedure result. For non-symmetric cases, the determination
of a such a class of Bayesian credible sets fills a gap in the literature and
includes an "equal-tails" modification of the HPD procedure. Several examples
are presented demonstrating wide applicability.
