The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple fi...

In safety-of-life applications of satellite navigation, the Protection Level (PL) equation translates what is known about the pseudorange errors into a reliable limit on the positioning error. The current PL equations for Satellite based augmentation systems are based on Gaussian statistics: all errors are characterized by a zero mean Gaussian distribution which is an upper bound of the true di...

Often in biomedical studies, the routine use of linear mixed-effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew-normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral-load measures in ...

We establish limit theorems for component–wise maxima of independent and identically distributed heavy–tailed processes. The focus here is on weak convergence in Hölder spaces. Given that the finite–dimensional distributions converge, the classical tightness conditions of Lamperti apply, provided that one can control the tail–behavior of Hölder norms. Here, by using a powerful isomorphism theor...

For the GGGG1 queue with First-Come First-Served, it is well known that the tail of the sojourn time distribution is heavier than the tail of the service requirement distribution when the latter has a regularly varying tail. In contrast, for the MMGG1 queue with Processor Sharing, Zwart and Boxma 26 showed that under the same assumptions on the service requirement distribution, the two tails ar...

Empirical studies have observed non-Gaussian behavior in pseudorange correction errors for the Local Area Augmentation System (LAAS). This paper introduces an overbounding technique, called core overbounding, designed to validate integrity for error distributions with heavier than Gaussian tails. The core overbounding process generates a conservative representation of the actual error distribut...

In this paper, we propose to include Weibull tail-distributions in a more general family of distributions. In particular, the considered model also encompasses the whole Fréchet maximum domain of attraction as well as log-Weibull tail-distributions. The asymptotic normality of some tail estimators based on the log-spacings between the largest order statistics is established in a unified way wit...

Let (Xn) be a sequence of independent and identically distributed random variables, with common absolutely continuous distribution F . An observation Xn is a near-record if Xn ∈ (Mn−1 − a, Mn−1], where Mn = max{X1, . . . , Xn} and a > 0 is a parameter. We analyze the point process η on [0,∞) of near-record values from (Xn), showing that it is a Poisson cluster process. We derive the probability...