Extended fractional cumulative past and paired <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e3175" altimg="si3.svg"><mml:mi>ϕ</mml:mi></mml:math>-entropy measures

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,&nbsp;Misagh et al. (2011) proposed a weighted information which is based on the cumulative&nbsp;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&nbsp;obtain some bounds for that. In order to ...

Bivariate Extension of Past Entropy

Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models a...

Measures of maximal entropy

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

On the Discrete Cumulative Residual Entropy