On Estimating the Residual Rényi Entropy under Progressive Censoring

Abstract

In this article, the residual Rényi entropy (RRE) as a measure of uncertainty is considered in progressively Type II censored samples and some properties of it are investigated. The RRE of sth order statistic from a continuous distribution function is represented in terms of the RRE of the sth order statistic from uniform distribution. In general, we do not have a closed form for RRE of order statistics in most of distributions. This gives us a motivation for obtaining some bounds for RRE in progressively censored samples. In addition, two estimators are proposed for RRE. The performance of these estimators is compared using simulation studies.

Keywords:

• Progressive censoring
• Rényi entropy
• Residual lifetime

Mathematics Subject Classification:

• 62G05; 62N02; 62N05