Some properties of cumulative Tsallis entropy

The cumulative entropy is an information measure which is alternative to the differential entropy. Indeed, the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. In this paper we propose a new generalized cumulative entropy based on Tsallis entropy (CTE) and its dynamic version (DCTE). We study some properties and characterization results for this measure

Cumulative measures of information and stochastic orders

In this paper we present some known results on cumulative measures of information, study their properties and relate these definitions to concepts of reliability theory. We give some relations of these measures of discrimination with some well-known stochastic orders and with the relative reversed hazard rate order. We investigate also a stochastic comparison among the empirical cumulative measures that can be related to the cumulative measures. Large part of this paper is a survey article; however, in the last section, we define a new measure of discrimination between residual lifetimes and study some of its properties

On Weighted Nwikpe Distribution: Properties and Applications

In this article, two-parameter continuous distribution is introduced. The proposed distribution is obtained by using a weight technique and is referred to as weighted Nwikpe distribution. This distribution is a generalization of baseline distribution that is Nwikpe distribution. Some structural properties of the distribution are derived. These are density function, distribution function, and reliability function, hazard rate function, moments, moment generating function, entropies, order statistics, Bonferroni and Lorenz curves. The method of maximum likelihood estimation has been established for investigating the parameters of the model. The behaviour of the parameters of the distribution is examined by a simulation study. Real data set is used to determine whether the weighted Nwikpe distribution is better than other well-known distributions in modeling data or not

Past Lifetime and Inactivity Time: from Entropy to Coherent Systems

Information Theory was originally proposed by Claude Shannon in 1948 in the landmark paper entitled "A Mathematical Theory of Communication". In this paper the concept of entropy was adopted for the first time in a field other than thermodynamics and statistical mechanics. Since then, the interest in entropy has grown more and more and the current literature now focuses mainly on the analysis of residual lifetime. However, in recent years the interest has 'changed direction'. New notions of entropy have been introduced and are used to describe the past lifetime and the inactivity time of a given system or of a component that is found not to be working at the current time. Moreover inferences about the history of a system may be of interest in real life situations. So, the past lifetime and the inactivity time can also be analysed in the context of the theory of coherent systems