A note on the cumulant approximation of entropy estimate

Entropy is the basic concept of information theory. It is well defined for random variables with known probability density function(pdf). For given data with unknown pdf, entropy should be estimated. Usually, estimation of entropy is based on the approximations of random quantities. In this paper, we investigate a cumulant approximation method for the entropy estimation and examine some interesting properties contained in it. Several distributions with the change of parameters of each distribution is considered for the investigation of pros and cons for the cumulant approximation. Comparison is also made with the true entropy.