Related papers: Power-law cross-correlations estimation under heav…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete…
Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…
The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…
In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal…
The detrended cross-correlation coefficient $\rho_{\rm DCCA}$ has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers…
Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…
This paper addresses the problem of estimating the tail index of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A…
The recent availability of electronic datasets containing large volumes of communication data has made it possible to study human behavior on a larger scale than ever before. From this, it has been discovered that across a diverse range of…
We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…
Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but…
Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by…
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in…
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…