Some Results on Dynamic Generalized Survival Entropy

Abstract

Recently, Zografos and Nadarajah (2005) proposed two measures of uncertainty based on the survival function, called the survival exponential entropy and the generalized survival exponential entropy. In this article, we explore properties of the generalized survival entropy and the dynamic version of it. We study conditions under which the generalized survival entropy of first order statistic can uniquely determines the parent distribution. The exponential, Pareto, and finite range distributions, which are commonly used in reliability, have been characterized using this generalized measure. Another measure of entropy is also introduced in analogy with cumulative entropy which has been proposed by Di Crescenzo and Longobardi (2009) and some properties of it are given.

Keywords:

• Failure entropy
• Generalized failure entropy
• Characterization
• First-order statistic
• Cumulative residual entropy
• Cumulative entropy

Mathematics Subject Classification:

• 94A17
• 62E10