Antonio Di Crescenzo

Abstract: In analogy with the cumulative residual entropy recently proposed by Wang et al. [2003a. A new and robust information theoretic measure and its application to image alignment. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science, vol. 2732, Springer, Heidelberg, pp. 388–400; 2003b. Cumulative residual entropy, a new measure of information and its application to image alignment. In: Proceedings on the Ninth IEEE International Conference on Computer Vision (ICCV’03), vol. 1, IEEE Computer Society Press, Silver Spring, MD, pp. 548–553], we introduce and study the cumulative entropy, which is a new measure of information alternative to the classical differential entropy. We show that the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X . Hence, our measure is particularly suitable to describe the information in problems related to ageing properties of reliability theory based on the past and on the inactivity times. Our results include various bounds to the cumulative entropy, its connection to the proportional reversed hazards model, and the study of its dynamic version that is shown to be increasing if the mean inactivity time is increasing. The empirical cumulative entropy is finally proposed to estimate the new information measure.

Abstract: As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

Abstract: The proportional reversed hazards model consists in describing random failure times by a family {[F(x)] θ , θ>0} of distribution functions, where F(x) is a baseline distribution function. We show various results on this model related to some topics in reliability theory, including ageing notions of random lifetimes, comparisons based on stochastic orders, and relative ageing of distributions.

Abstract: We consider a “length-biased” shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of “weighted residual entropy” and “weighted past entropy”, that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively. The obtained results include their behaviors under monotonic transformations. AMS Classification: 62N05, 62B10

Abstract: On the basis of Kullback–Leibler discrimination information and of discrimination information introduced by Ebrahimi and Kirmani (Ann. Inst. Statist. Math. 48 (1996a) 257), we propose a measure of discrepancy between past-life distributions. Some properties of this measure are studied and a characterization of the proportional reversed hazards model through such a measure is given.

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Abstract: Technical foundations introduction software reliability and system reliability the operational profile software reliability modelling survey model evaluation and recalibration techniques practices and experiences best current practice of SRE software reliability measurement experience measurement-based analysis of software reliability software fault and failure classification techniques trend analysis in validation and maintenance software reliability and field data analysis software reliability process assessment emerging techniques software reliability prediction metrics software reliability and testing fault-tolerant SRE software reliability using fault trees software reliability process simulation neural networks and software reliability. Appendices: software reliability tools software failure data set repository.