Extreme Points of the Core of Possibility Measures and Maxitive p-Boxes

Under an epistemic interpretation, an upper probability can be regarded as equivalent to the set of probability measures it dominates, sometimes referred to as its core. In this paper, we study the properties of the number of extreme points of the core of a possibility measure, and investigate in detail those associated with (uni- and bi-)variate p-boxes, that model the imprecise information about a cumulative distribution function.

Weighted Regret-Based Likelihood: A New Approach to Describing Uncertainty

Recently, Halpern and Leung suggested representing uncertainty by a set of weighted probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E'. In this paper, a notion of comparative likelihood when uncertainty is represented by a set of weighted probability measures is defined. It generalizes the ordering defined by probability (and by lower probability) in a natural way; a generalization of upper probability can also be defined. A complete axiomatic characterization of this notion of regret-based likelihood is given.

Weak and Strong Limit Theorems for Stochastic Processes under Nonadditive Probability

This paper extends laws of large numbers under upper probability to sequences of stochastic processes generated by linear interpolation. This extension characterizes the relation between sequences of stochastic processes and subsets of continuous function space in the framework of upper probability. Limit results for sequences of functional random variables and some useful inequalities are also obtained as applications.

On normality assumptions for claims in insurance

The aim of this paper is to discuss effects of deviations from hypothetized normality. Two models are considered, one is the first pension pillar (and we consider here very small samples, which plays some role at start of some pension system or at early phases of it) and second one of modeling for IBNR (here we consider mid-samples). We will show that at early phases of 1stpension pillar in Slovakia the estimation of upper probability of oversizing of critical constant given by Potocký and Stehlík, 2005, fits well. For the case of IBNR reserves, the date given by Stelljes, 2006, are significantly more skewed and thus further research is needed for appropriate modelling of these reserves.

Non-parametric prediction of unobserved failure modes

This paper presents the application of a recently developed non-parametric predictive inferential approach for multinomial data to the problem of prediction of occurrence of new failure modes. These inferences are in terms of lower and upper probabilities for the next observation. The lower probability of occurrence of a new failure mode is zero in all cases, as the data never suggest strongly that there have to be further failure modes. The main interest is in the upper probability that the next observed failure is caused by a new failure mode.

INCLUSIVENESS MEASUREMENT OF RANDOM EVENTS USING ROUGH SET THEORY

In some probabilistic problems, complete information about the probability model may not exist. In this article, we obtain a lower and upper probability for an arbitrary event by using rough set theory and then a measurement for inclusiveness of events is introduced.