181 research outputs found
Aging functions and multivariate notions of NBU and IFR
No full textFor 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
Interactions between ageing and risk properties in the analysis of burn-in problems
No full textSeveral 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
Threshold copulas and positive dependence
No full textStarting with a notion of positive dependence View the MathML source and with the family of the lower threshold copulas Ct associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas Ct for some t.
Then, we analyze some structural aspects of lower threshold copulas and of the given definitions. Furthermore we consider several specific cases arising from relevant special choices of View the MathML source (e.g., PQD, LTD, TP2 and PLR). Our analysis, in particular, allows us to present a number of relevant examples and counter-examples, which can be useful in the study of the tail dependence for a bivariate distribution
Extension of dependence properties to semi-copulas and applications to the mean-variance model
No full textThis 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. (C) 2012 Elsevier B.V. All rights reserved
A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts
No full textIn this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess-of-loss and of a proportional type. The stochastic structure of the set of pairs (claim’s arrival time, claim’s size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract
Subjective probability models for lifetimes
No full textBayesian methods in reliability cannot be fully utilized and understood without full comprehension of the essential differences that exist between frequentist probability and subjective probability. Switching from the frequentist to the subjective approach requires that some fundamental concepts be rethought and suitably redefined. Subjective Probability Models for Lifetimes details those differences and clarifies aspects of subjective probability that have a direct influence on modeling and drawing inference from failure and survival data. In particular, within a framework of Bayesian theory, the author considers the effects of different levels of information in the analysis of the phenomena of positive and negative aging.The author coherently reviews and compares the various definitions and results concerning stochastic ordering, statistical dependence, reliability, and decision theory. He offers a detailed but accessible mathematical treatment of different aspects of probability distributions for exchangeable vectors of lifetimes that imparts a clear understanding of what the "probabilistic description of aging" really is, and why it is important to analyzing survival and failure data
A Concept of Duality for Multivariate Exchangeable Models
No full textIn some past works by the author and collaborators, the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed. Generally, the ageing function turns out to be a semi-copula. Here we focus attention on the special class of survival models whose ageing function is actually a copula. For pairs of models in this class we define a notion of duality. Such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula. The formulation of the notion of duality presented here came out some years ago, in the frame of research activity in collaboration with Bruno Bassan
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