  In this paper we consider the stacking of isotonic regression and the method
of rearrangement with the empirical estimator to estimate a discrete
distribution with an infinite support. The estimators are proved to be strongly
consistent with $\sqrt{n}$-rate of convergence. We obtain the asymptotic
distributions of the estimators and construct the asymptotically correct
conservative global confidence bands. We show that stacked Grenander estimator
outperforms the stacked rearrangement estimator. The new estimators behave well
even for small sized data sets and provide a trade-off between goodness-of-fit
and shape constraints.
