Black swans or dragon kings? A simple test for deviations from the power law

We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime ($0<\alpha\le 2$). In this paper we illustrate that widely used tail index estimates (log-log linear regression and Hill) can give exponents well above the asymptotic limit for $\alpha$ close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent $\alpha$ around 3 may very well indicate a Levy-stable distribution with $\alpha\approx 1.8$.Comment: To be published in Int. J. Modern Physics C (2001) vol. 12 no.

Universal relaxation function in nonextensive systems

We have derived the dipolar relaxation function for a cluster model whose volume distribution was obtained from the generalized maximum Tsallis nonextensive entropy principle. The power law exponents of the relaxation function are simply related to a global fractal parameter $\alpha$ and for large time to the entropy nonextensivity parameter $q$. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived from an extension of the Levy central limit theorem. They are in full agreement with the Jonscher universality principle. Moreover our model gives a physical interpretation of the mathematical parameters of the Weron stochastic theory and opens new paths to understand the ubiquity of self-similarity and power laws in the relaxation of large classes of materials in terms of their fractal and nonextensive properties.Comment: Two figures. Submitted for publicatio

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power-law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. We also in terms of the DEA revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description.Comment: 16 pages, 7 figure

Energy-Aware Cloud Management through Progressive SLA Specification

Novel energy-aware cloud management methods dynamically reallocate computation across geographically distributed data centers to leverage regional electricity price and temperature differences. As a result, a managed VM may suffer occasional downtimes. Current cloud providers only offer high availability VMs, without enough flexibility to apply such energy-aware management. In this paper we show how to analyse past traces of dynamic cloud management actions based on electricity prices and temperatures to estimate VM availability and price values. We propose a novel SLA specification approach for offering VMs with different availability and price values guaranteed over multiple SLAs to enable flexible energy-aware cloud management. We determine the optimal number of such SLAs as well as their availability and price guaranteed values. We evaluate our approach in a user SLA selection simulation using Wikipedia and Grid'5000 workloads. The results show higher customer conversion and 39% average energy savings per VM.Comment: 14 pages, conferenc

Ferromagnetic fluid as a model of social impact

The paper proposes a new model of spin dynamics which can be treated as a model of sociological coupling between individuals. Our approach takes into account two different human features: gregariousness and individuality. We will show how they affect a psychological distance between individuals and how the distance changes the opinion formation in a social group. Apart from its sociological aplications the model displays the variety of other interesting phenomena like self-organizing ferromagnetic state or a second order phase transition and can be studied from different points of view, e.g. as a model of ferromagnetic fluid, complex evolving network or multiplicative random process.Comment: 8 pages, 5 figure

Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission

A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy statistics of soft X-ray solar flares for class M and C is well described by a FARIMA time series with Pareto innovations. The model is characterized by two effects. One of them is a long-range dependence (long-term memory), and another corresponds to heavy-tailed distributions. Their parameters are statistically stable enough during the periods. However, when the solar activity tends to minimum, they change essentially. We discuss possible causes of this evolution and suggest a statistical model for predicting the flare energy statistics.Comment: 21 pages, 7 figure

Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.Comment: 5 pages; 3 figures; corrected versio