We introduce a method to estimate the failure time of a class of weighted k -out-of- n systems using the idea of rational expectations, which to the best of our knowledge is a new approach, not found elsewhere in the existing literature. This paper explores the predictive power of several statistical indicators (variance, skewness, kurtosis, Gini coefficient, entropy) and shows how they perform differently as the system approaches global failure. The proposed method is shown to outperform a benchmark prediction model obtained without rational expectations, and our results offer a panoramic view of the predictive power of the statistical indicators under different assumptions about the initial weight distributions.

Abstract This paper introduces a new dissimilarity measure between two discrete and finite probability distributions. The followed approach is grounded jointly on mixtures of probability distributions and an optimization procedure. We discuss the clear interpretation of the constitutive elements of the measure under an information-theoretical perspective by also highlighting its connections with the Rényi divergence of infinite order. Moreover, we show how the measure describes the inefficiency in assuming that a given probability distribution coincides with a benchmark one by giving formal writing of the random interference between the considered probability distributions. We explore the properties of the considered tool, which are in line with those defining the concept of quasimetric—i.e. a divergence for which the triangular inequality is satisfied. As a possible usage of the introduced device, an application to rare events is illustrated. This application shows that our measure may be suitable in cases where the accuracy of the small probabilities is a relevant matter.

This paper deals with the theoretical analysis of the long-term memory property of time series generated by the aggregation of heterogeneous terms. The diversity is captured by the different features, regarding the persistence of each component. It is shown that the memory of the aggregation is driven by the one related to some key components. The argument is carried out by developing an equilibrium model for asset prices in a financial market with heterogeneous agents. © 2011 Wiley Periodicals, Inc.