This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...

An important characteristic of any TCP connection is the sequencing of packets within that connection. Out-of sequence packets indicate that the connection suffers from loss, duplication or reordering. More generally, in many distributed applications information integrity requires that data...

For testing whether a distribution function is heavy tailed, we study the Kolmogorov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations. The score test and the integrated score test show the best performance. Although...

In this work we introduce a generalization of the slash distribution using beta-normal distribution. This newly defined generalization is more flexible than the ordinary slash distribution and contains distributions that can be not only symmetric and unimodal, but also asymmetric and bimodal. We...

This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index α is in (0,2), equal to 2, and in (2,∞), respectively. The partial sum weakly...

An important characteristic of any TCP connection is the sequencing of packets within that connection. Out-of sequence packets indicate that the connection suffers from loss, duplication or reordering. More generally, in many distributed applications information integrity requires that data...

Hall & Yao (2003) showed that, for ARCH/GARCH, i.e. autoregressive conditional heteroscedastic/generalised autoregressive conditional heteroscedastic, models with heavy‐tailed errors, the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow...

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally...

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of...

With respect to the climate change, and more generally to the energy problem, in the laboratories working on the subject, scientists contribute to clarify the situation and to help decision makers by yielding and updating factual physical informations, and also by modelling. This conceptual work...