  We compare an entropy estimator $H_z$ recently discussed in [10] with two
estimators $H_1$ and $H_2$ introduced in [6][7]. We prove the identity $H_z
\equiv H_1$, which has not been taken into account in [10]. Then, we prove that
the statistical bias of $H_1$ is less than the bias of the ordinary likelihood
estimator of entropy. Finally, by numerical simulation we verify that for the
most interesting regime of small sample estimation and large event spaces, the
estimator $H_2$ has a significant smaller statistical error than $H_z$.
