In practice, Financial Time Series have serious volatility cluster, that is large volatility tend to be concentrated in a certain period of time, and small volatility tend to be concentrated in another period of time. While GARCH models can well describe the dynamic changes of the volatility of financial time series, and capture the cluster and heteroscedasticity phenomena. At the beginning of ...

Estimating parameters in heavy-tailed distribution plays a central role in extreme value theory. It is well known that classical estimators based on the first order asymptotics such as the Hill, rank-based and QQ-estimators are seriously biased under finer second order regular variation framework. To reduce the bias, many authors proposed the so-called second order reduced bias estimators for b...

For the M=G=1 uid model the stationary distribution of the buuer content is investigated for the case that the message length distribution B(t) has a Pareto-type tail, i.e. behaves as 1 ? O(t ?) for t ! 1 with 1 < < 2. This buuer content distribution is closely related to the stationary waiting time distribution W (t) of a stable M=G=1 model with service time distribution B(t), in particular wh...

We exhibit a new stability property of Weibull tail-distributions. It is shown that the power of a random variable with a Weibull tail-distribution still has a Weibull tail-distribution and the associated Weibull tail-coefficient is exhibited. Weibull tail-distributions are defined through their distribution function by:

BACKGROUND Gene, protein, or metabolite expression levels are often non-normally distributed, heavy tailed and contain outliers. Standard statistical approaches may fail as location tests in this situation. OBJECTIVES In three Monte-Carlo simulation studies, we aimed at comparing the type I error levels and empirical power of standard location tests and three adaptive tests [O'Gorman, Can J S...

One of the key invariants in computer and communication systems is that im¬ portant characteristics follow long-or heavy-tailed distributions. This means that the tail of these distributions declines according to a power law. Hence, the probability for extremely large values is non-negligible. For example, such distributions have been found to describe the size of web objects or the pro¬ cessin...