Cumulative Paired φ-Entropy

Cumulative Paired φ-Entropy

Abstract: A new kind of entropy will be introduced which generalizes both the differential entropy and the cumulative (residual) entropy. The generalization is twofold. First, we simultaneously define the entropy for cumulative distribution functions (cdfs) and survivor functions (sfs), instead of defining it separately for densities, cdfs, or sfs. Secondly, we consider a general “entropy gener...

Some Results on Weighted Cumulative Entropy

Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, Misagh et al. (2011) proposed a weighted information which is based on the cumulative entropy called Weighted Cumulative Entropy (WCE). The above-mentioned model is a Shiftdependent Uncertainty Measure. In this paper, we examine some of the properties of WCE and obtain some bounds for that. In order to ...

On the Discrete Cumulative Residual Entropy

Monitoring paired binary surgical outcomes using cumulative sum charts.

Correlated binary data are encountered in many areas of medical research, system reliability and quality control. For monitoring failures rates in such situations, simultaneous bivariate cumulative sum (CUSUM) charts with the addition of secondary control limits are proposed. Using an approach based on a Markov chain model, the run length properties of such a monitoring scheme can be determined...

Subadditivity of Matrix Φ-entropy and Concentration of Random Matrices

Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities.