Stacked Grenander and rearrangement estimators of a discrete distribution

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