An Extension of Generalized Cumulative Residual Entropy

Abstract

In this paper, a new extension of cumulative residual entropy is proposed. It contain the generalized cumulative residual entropy introduced by Psarrakos and Navarro (2013) and is related with the k-record values. We also consider a dynamic version of this new cumulative residual entropy using the residual lifetime. For these concepts, we obtain some properties similar to generalized cumulative residual entropy in stochastic ordering and aging classes properties.

Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values

“…We note that the sequence of k-th upper record times is denoted as {U n(k) , n ≥ 1}. It is defined similarly to T n(k) by reverting the last inequality in (6) (see, for instance, Dziubdziela and Kopociński [14] or Tahmasebi et al [16]). Record values apply in problems such as industrial stress testing, meteorological analysis, hydrology, sport, and economics.…”

Interval-Valued Uncertainty Based on Entropy and Dempster–Shafer Theory

“…Obviously, in the analysis process of the system performance, uncertainty appears at different steps of analysis and the interaction between these sources of uncertainty cannot be modeled easily. Thus, in order to evaluate and reduce uncertainty, different models and modern mathematical frameworks have been proposed to quantify both aleatory and epistemic uncertainties in systems (e.g., see [24,25]). However, the existing methods to evaluate the effect of mixed uncertainty using a piece of information and different mathematical frameworks are efficient, and modern frameworks for mathematical representation of uncertainty are still under development.…”