Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property

We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate ageing. A specific feature of such an approach dwells on the concept of semi-copula and in the extension, from copulas to semi-copulas, of properties of stochastic dependence. In this perspective, we aim to discuss some intricate aspects of conceptual character and to provide the readers with pertinent remarks from a Bayesian Statistics standpoint. In particular we will discuss the role of extensions of dependence properties. "Archimedean" models have an important role in the present framework. In the second part of the paper, the definitions of Kendall distribution and of Kendall equivalence classes will be extended to semi-copulas and related properties will be analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean" models and extend to them the analysis of the relations between the ageing notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD

Multivariate negative aging in an exchangeable model of heterogeneity

We introduce an exchangeable model, which accounts for heterogeneity and dependence at a time. Based on this model, we show how situations of multivariate negative ageing arise in a natural way from conditions of heterogeneity

Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes

As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case, we assume that $T_{1},...,T_{r}$ are identically distributed, with a common survival function $\overline{G}$ and their survival copula is denoted by $K$. The diagonal's and subdiagonals' sections of $K$, along with $\overline{G}$, are possible tools to describe the information needed to recover the laws of order statistics. When attention is restricted to the absolutely continuous case, such a joint distribution can be described in terms of the associated multivariate conditional hazard rate (m.c.h.r.) functions. We then study the distributions of the order statistics of $T_{1},...,T_{r}$ also in terms of the system of the m.c.h.r. functions. We compare and, in a sense, we combine the two different approaches in order to obtain different detailed formulas and to analyze some probabilistic aspects for the distributions of interest. This study also leads us to compare the two cases of exchangeable and minimally stable variables both in terms of copulas and of m.c.h.r. functions. The paper concludes with the analysis of two remarkable special cases of stochastic dependence, namely Archimedean copulas and load sharing models. This analysis will allow us to provide some illustrative examples, and some discussion about peculiar aspects of our results

Strategie differenziate nelle popolazioni target: I bambini [Strategies for cardiovascular prevention in children]

L’obesità, insieme ad abitudini alimentari scorrette e comportamenti sedentari, rappresenta un fattore di rischio per le malattie cardiovascolari. Per programmare interventi di prevenzione dell’obesità infantile e valutarne l’efficacia è necessario disporre di validi sistemi di sorveglianza. OKkio alla SALUTE si inserisce in questo contesto con lo scopo di descrivere la variabilità geografica e l’evoluzione temporale della stato ponderale dei bambini delle scuole primarie in Italia, degli stili alimentari, della pratica dell’attività fisica1. Con OKkio alla SALUTE, l’Italia partecipa al progetto europeo European Childhood Obesity Surveillance Initiative, coordinato dal WHO Regione Europea, che prevede indagini epidemiologiche ripetute a cadenza regolare sui bambini di età 6-9 anni che frequentano la scuola primaria. Nel contesto italiano, OKkio alla SALUTE è parte integrante del progetto “Sistema di indagini sui rischi comportamentali in età 6-17 anni” promosso e finanziato nel 2007 dal Centro Nazionale per la Prevenzione e il Controllo delle Malattie (CCM) del Ministero della Salute e affidato al coordinamento del Centro Nazionale di Epidemiologia, Sorveglianza e Promozione della Salute (CNESPS) dell’Istituto Superiore di Sanità (ISS)