Related papers: Distributional Tail Estimation Through Its Charact…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus…
The replacement of indicator functions by integrated beta kernels in the definition of the empirical stable tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but…
We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…
We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.
The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…
To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…
Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…
Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual…
Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…
A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…
The aim of a probabilistic output analysis is to derive a probability distribution of possible output values for a program from a probability distribution of its input. We present a method for performing static output analysis, based on…