1,721,005 research outputs found
Dependence and aging properties of lifetimes with Schur-constant survival functions
Full text linkFor n-dimensional survival functions, we study some probabilistic aspects of the Schur-constant property. The latter is of interest in that it extends the “lack-of-memory” property in a Bayesian context. Some general facts are studied in detail, and related results about interdependence, aging, and extendibility are presented
A spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contracts
Full text linkIn 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
A Concept of Dynamic Sufficiency and Optimal Stopping of Longitudinal Observations in Lifetimes
No full textWhat About the Posterior Distributions When the Model is Non-dominated?
No full textStarting from the first inception of philosophical research that had subsequently led to subjective probability and Bayesian statistics, and to date the most recent developments, the probabilistic nature and the related statistical implications of Bayes theorem have been thoroughly discussed. However, the substantial contents of such a formula is very deep and new contributions are still continuing after 250 years. The simplest form of Bayes theorem is met when dominated statistical models are dealt with. This is, in a sense, comfortable, specially as far as parametric models are considered. Actually, most statistical techniques in the frame of parametric inference refer to dominated statistical models. Different problems in the applications, however, can lead to considering non-dominated models. In these cases, some complications and intriguing conclusions can arise. Concerning non-dominated statistical models, we devote this note to discussing some mathematical features that may sometimes escape the attention of statisticians. We deal with questions and results that, at a first glance, may appear of almost-exclusive measure-theoretic interest. However, they have a real statistical meaning of their own and the present note aims to stimulate some reflections about this field
WBF property and stochastical monotonicity of the Markov process associated to Schur-constant survival functions
Full text linkWe concentrate attention on non-negative absolutely continuous random variables with a Schuu-constant joint survival function. Such a property defines a special case of exchangeability, corresponding to a multivariate no aging condition, in a Bayesian set-up. In the longitudinal observation of our random variables, the pair (Number of failures, Total time on test) is a Markov process which has a central role. Our main result result shows that such a process is stochastically increasing if and only if the variables are WBF (Weakened By Failure). (C) 1996 Academic Press, Inc
Merging Exchangeable Occupancy Distributions: The Family M^(a) and its Connection with the Maximum Entropy Principle
No full textIn this paper a new transformation of occupancy distributions, called merging, is introduced. In particular, it will be studied the effect of merging on a class of occupancy distributions that was recently introduced in Collet et al. (Probab Eng Inf Sci. 27:533-552 2013). These results have an interesting interpretation in the so-called entropy maximization inference. The last part of the paper is devoted to highlight the impact of our findings in this research area
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
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