(Generalized) Maximum Cumulative Direct, Residual, and Paired Φ Entropy Approach

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...

On the Discrete Cumulative Residual Entropy

Quantile Approach of Generalized Cumulative Residual Information Measure of Order $(alpha,beta)$

In this paper, we introduce the concept of quantile-based generalized cumulative residual entropy of order $(alpha,beta)$ for residual and past lifetimes and study their properties. Further we study the proposed information measure for series and parallel system when random variable are untruncated or truncated in nature and some characterization results are presented. At the end, we study gene...

Generalized Maximum Entropy

A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this probiem, advocated by E.T. Jaynes [1], is to igriore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic M...

Generalized maximum entropy estimation

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme using a smoothed fast gradient method that is equipped with explicit bounds on the approximation error. We further demonstrate how the prese...