Change point models and conditionally pure birth processes; an inequality on the stochastic intensity

We analyze several aspects of a class of simple counting processes, that can emerge in some fields of applications where the presence of a change-point occurs. Under simple conditions we, in particular, prove a significant inequality for the stochastic intensity.Comment: 15 page

Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing

Interactions between ageing and risk properties in the analysis of burn-in problems

Several relevant problems in reliability can be looked at as problems of risk management and of decisions in the face of uncertainty. However, in this frame, the so-called burn-in problem can be seen as a problem of risk taking par excellence. In this paper, we in particular point out some aspects concerning interactions between the probabilistic model for lifetimes and considerations of an economic kind. As one of the features of our work, we hinge on some unexplored connections between ageing properties of a one-dimensional survival function Formula and risk-aversion-type properties of the function u(t) = bG(t), b > 0, when the latter is seen as a utility function

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

Aging functions and multivariate notions of NBU and IFR

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals

Extension of dependence properties to semi-copulas and applications to the mean–variance model

This paper deals with the construction of a semi-copula D, not necessarily exchangeable, whose “dependence” properties translate remarkable aspects of investors’ behavior. To achieve this aim, we propose a new version of the standard mean-variance framework. For our purpose, a particular class of utility functions G has been introduced. The induced transformation of G is considered and the definition of semi-copula D hinges on the family of the indifference curves of G

Relations Between Stochastic Orderings and generalized Stochastic Precedence

The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence and analyze its relations with the notions of stochastic ordering. Such a study leads us to introducing some special classes of bivariate copulas. Motivations for our study can arise from different fields. In particular we consider the frame of Target-Based Approach in decisions under risk. This approach has been mainly developed under the assumption of stochastic independence between "Prospects" and "Targets". Our analysis concerns the case of stochastic dependence.Comment: 13 pages, 6 figure

On modular decompositions of system signatures

Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. This $n$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the $n$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results

Comportamenti delle famiglie e work-life balance.Il ruolo dell'offerta di trasporti

Negli ultimi decenni si è registrato in vari Paesi un forte incremento del numero di famiglie con presenza di genitori entrambi lavoratori. Inoltre si è evidenziata una maggior propensione a coltivare delle attività extralavorative per il completamento della soddisfazione personale. Allo stesso tempo le difficoltà legate al traffico e all'offerta di trasporti pubblici rappresentano ancora un problema in un grande numero di centri urbani. Ciò pone sempre più frequentemente la questione di come si possano conciliare le esigenze di vita professionale con quelle familiari e private, in un contesto di benessere personale, e trovare quello che viene chiamato il 2 work-family balance. Per questo motivo policy makers e aziende sono chiamate ad impegnarsi in proposte e soluzioni di idonee politiche di welfare. La conciliazione tra vita familiare e lavorativa è strettamente congiunta alle caratteristiche urbanistiche della zona in cui si vive e si lavora ed alle scelte in tema di servizi di trasporto. Individuare quindi quali siano i comportamenti e le preferenze in questi ambiti è fondamentale per strutturare e suggerire delle policy efficienti. Da un punto di vista della ricerca scientifica quanto appena detto si riflette nell’interazione tra diversi filoni della ricerca. Scopo del presente articolo è quindi quello di analizzare la letteratura esistente che abbia precedentemente indagato, possibilmente in modo congiunto, il tema della conciliazione tra vita familiare e lavorativa e quello delle scelte in tema di trasporti e pianificazione urbana. Particolare attenzione sarà dedicata a quella parte della letteratura, che in modo innovativo rispetto al passato, abbia analizzato oltre alle scelte individuali anche le interazione dei gruppi, come ad esempio le famiglie.

Aggregation and signature based comparisons of multi-state systems via decompositions of fuzzy measures

© 2019 This document is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the accepted version of a published work that appeared in final form in Fuzzy Sets and SystemsIn the reliability literature, several results have been presented to compare binary (two states) systems. Often, such results are obtained from copula-based extensions of fuzzy measures, where a fuzzy measure describes the structure of a system and a copula describes the stochastic dependence among the lifetimes of its components. Other similar results have been obtained in terms of the concept of signature. Here, we extend all those results to multi-state systems made up from binary components by suitably constructing corresponding mixed binary systems. For such a construction, we show how any fuzzy measure can be decomposed as a convex combination of {0,1}-valued fuzzy measures and how such a decomposition extends to the corresponding aggregation function. For a mixed system we can furthermore consider its signature and so we can also define a signature for the multi-state system. For mixed systems associated to different multi-state systems, we can thus obtain different comparison results, which can be translated into the corresponding comparisons for the parent multi-state systems. Stochastic comparisons are obtained for the discrete random variables which represent the states of two systems at time t, as well. The arguments in the paper will be illustrated by means of examples and related remarks