  We present two new estimators for estimating the entropy of absolutely
continuous random variables. Some properties of them are considered,
specifically consistency of the first is proved. The introduced estimators are
compared with the existing entropy estimators. Also, we propose two new tests
for normality based on the introduced entropy estimators and compare their
powers with the powers of other tests for normality. The results show that the
proposed estimators and test statistics perform very well in estimating entropy
and testing normality. A real example is presented and analyzed.
