Novel entropy estimators of a continuous random variable

Abstract

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling (SRS), ranked set sampling (RSS), and double RSS (DRSS) schemes. The theoretical results of the proposed entropy estimators are derived. The proposed entropy estimators are compared in terms of the bias and the root mean squared errors, theoretically and numerically, with the Vasicek O. [A test for normality based on sample entropy, J. R. Stat. Soc. B 38:54–59, 1976.] entropy estimators using SRS, RSS, and DRSS schemes. It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.