Weighted entropy measures improve understanding of system aging
On Weighted Mathai-Haubold Entropy Measures
Information Theory
Summary
Entropy measures help us understand randomness or uncertainty in systems. This paper introduces new weighted versions of a type of entropy called Mathai-Haubold entropy and looks at how these can describe how systems age or change over time. The authors also create formulas to estimate these new measures without relying on strict assumptions and test how accurate these estimates are by running computer simulations. Their work helps provide new mathematical tools to study and measure changes in uncertain systems more effectively.
entropyweighted entropyMathai-Haubold entropyresidual entropypast entropyaging classesnon-parametric estimationMonte-Carlo simulationbiasmean squared error
Authors
Oindrali Das, Siddhartha Chakraborty
Abstract
In this paper, we propose weighted Mathai-Haubold entropy along with their residual and past versions and study their properties. We develop aging classes based on the weighted Mathai-Haubold residual and past entropy measures. Also, some inequalities related to the three proposed measures are discussed. Non-parametric estimators of the proposed measures are introduced and their properties are investigated. Performance of this estimator is evaluated by means of bias and mean squared error using Monte-Carlo simulations.