Nonparametric Estimation of the Residual Entropy Function with Length-Biased Data

Document Type : Original Article


1 Department of Mathematics and Statistics, Mashhad Branch, Islamic Azad University,Mashhad, Iran.

2 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University ofMashhad, Mashahd, Iran.


We propose a nonparametric estimator for the residual entropy function based on length-biased data. Some asymptotic results have been proved. The strong consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to evaluate the performance of the estimator using the bias and mean-squared error. A real data set is considered, and we show that the data follow a length-biased distribution. Moreover, the proposed estimator yields a better value for the estimated residual entropy in comparison to the competitor estimator.


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Volume 21, Issue 1
June 2022
Pages 1-18
  • Receive Date: 23 December 2020
  • Revise Date: 13 September 2022
  • Accept Date: 05 October 2022