Cumulative Residual and Relative Cumulative Residual Fisher Information and Their Properties
Omid Kharazmi, N. Balakrishnan
Abstract
In this work, we propose cumulative residual Fisher information and relative cumulative residual Fisher information measures and establish some of their properties. We first show that these cumulative Fisher measures can be expressed based on the hazard function. We then define extended versions of cumulative residual entropy and cumulative residual Fisher information measures based on the Jensen inequality. We also discuss connections between these information measures based on a new version of de Bruijn's identity for survival functions.
Topics & Concepts
ResidualFisher informationResidual entropyMathematicsCumulative distribution functionStatisticsDe Bruijn sequenceEntropy (arrow of time)Discrete mathematicsAlgorithmProbability density functionStatistical physicsQuantum mechanicsConfiguration entropyPhysicsStatistical Distribution Estimation and ApplicationsStatistical Mechanics and EntropyMathematical Inequalities and Applications