119 research outputs found
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
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
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
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
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 . For such models, we study some properties of multivariate aging of that are described by means of the multivariate aging function , which is a useful tool for describing the level curves of . 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
Dependence Among Order Statistics for time-transformed exponential models
Let X1, ..., Xn be a random vector distributed according to a time-transformed exponential model. This is a special class of exchangeable models, which, in particular, includes multivariate distributions with Schur-constant survival functions. Let for 1 i n, Xi:n denote the corresponding ith-order statistic. We consider the problem of comparing the strength of dependence between any pair of Xi’s with that of the corresponding order statistics. It is in particular proved that for m = 2, ..., n, the dependence of X2:m on X1:m is more than that of X2 on X1 according to more stochastic increasingness (positive monotone regression) order, which in turn implies that X1:m, X2:mº is more concordant than X1, X2. It will be interesting to examine whether these results can be extended to other exchangeable models
Dependence Among Order Statistics for Time-transformed Exponential Models
Let (X1, . . . ,Xn) be a random vector distributed according to a time-transformed exponential model. This is a special class of exchangeable models, which, in particular, includes multivariate distributions with Schur-constant survival functions and with identical marginals. Let for 1 ≤ i ≤ n, Xi:n denote the corresponding ith order statistic. We consider the problem of comparing the strength of dependence between any pair of Xi’s with that of the corresponding order statistics. It is proved that for m = 2, . . . , n, the dependence of X2:m on X1:m is more than that of X2 on X1 according to more stochastic increasingness (positive monotone regression) order, which in turn implies that (X1:m,X2:m) is more concordant than (X1,X2). It will be interesting to examine whether these results can be extended to other exchangeable models
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