Estimation of Rényi entropy for lifetime uncertainty

Abstract

A system can be considered to be reliable if it operates successfully for a long period of time and has fewer uncertainties during its lifespan. In other words, lower the uncertainty of a random variable implies higher reliability [see Ebrahimi N. How to measure uncertaintyin the residual life time distribution. Sankhya: Indian J Stat SerA. 1996;58:48–57]. Motivated by this, the present study considers a generalized entropy function, namely the Rényi entropy in the quantile framework as a measure of uncertainty and proposes two nonparametric estimators for its computation. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study and real data analysis are carried out to compare the performance and usefulness of the estimators.

KEYWORDS:

• Rényi entropy
• quantile function
• nonparametric density estimation
• kernel density estimation
• MSE
• absolute bias

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Data availability statements

Authors can confirm that all relevant data are included in the article and/or its supplementary information files.

Additional information

Funding

The first author wishes to thank Cochin University of Science and Technology, India, for the financial support. The second author wishes to thank the Science and Engineering Research Board (SERB), Government of India (FILE NO.MTR/2020/000051 vide Diary No. SERB/F/ 5424/2020-2021) for the financial support.