  We explore the use of a sufficient statistic based on the identified members
that are obtained for samples that are selected under the $M_0$
capture-recapture closed population model (Schwarz and Seber, 1999). A
Rao-Blackwellized version of the estimator based on a sufficient statistic is
then presented. We explore the efficiency of the improved estimator via a
simulation study. The R code for the simulation is provided in the appendix.
