| Abstract: | In this paper, we first propose a new estimator of entropy for continuous random variables. Our estimator is obtained by correcting the coefficients of Vasicek's A test for normality based on sample entropy, J. R. Statist. Soc. Ser. B 38 (1976), pp. 54–59] entropy estimator. We prove the consistency of our estimator. Monte Carlo studies show that our estimator is better than the entropy estimators proposed by Vasicek, Ebrahimi et al. Two measures of sample entropy, Stat. Probab. Lett. 20 (1994), pp. 225–234] and Correa A new estimator of entropy, Commun. Stat. Theory Methods 24 (1995), pp. 2439–2449] in terms of root mean square error. We then derive the non-parametric distribution function corresponding to our proposed entropy estimator as a piece-wise uniform distribution. We also introduce goodness-of-fit tests for testing exponentiality and normality based on the said distribution and compare its performance with their leading competitors. |
