Related papers: Statistical outliers in random laser emission
A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns,…
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
We define outliers as a set of observations which contradicts the proposed mathematical (statistical) model and we discuss the frequently observed types of the outliers. Further we explore what changes in the model have to be made in order…
We search for outliers in extreme events of statistical size distributions of astrophysical data sets, motivated by the {\sl Dragon-King hypothesis} of Sornette (2009), which suggests that the most extreme events in a statistical…
We report the studies of emission from a novel random amplifying medium that we term a ``Levy Laser'' due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification…
When does the presence of an outlier in some measured property indicate that the outlying object differs qualitatively, rather than quantitatively, from other members of its apparent class? Historical examples include the many types of…
There are a number of mathematical formalisms of the term "outlier" in statistics, though there is no consensus on what the right notion ought to be. Accordingly, we try to give a consistent and robust definition for a specific type of…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…
Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…
We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. We also reintroduce the inward…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However,…
We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…
We develop the concept of ``dragon-kings'' corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These…
Bayesian statistics emphasizes the importance of prior distributions, yet finding an appropriate one is practically challenging. When multiple sample results are taken regarding the frequency of the same event, these samples may be…
We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes…
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to…
We present theoretical and experimental results of L\'evy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between…