Related papers: Tail behaviour of multiple random integrals and U-…
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 investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
Let $\Psi_1,\Psi_2,...$ be a sequence of i.i.d. random Lipschitz functions on a complete separable metric space with unbounded metric $d$ and forward iterations $X_n$. Suppose that $X_n$ has a stationary distribution. We study the…
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…
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…
We introduce $\zeta$- and $s$-values as quantile-based standardizations that are particularly suited for hypothesis testing. Unlike p-values, which express tail probabilities, $s$-values measure the number of semi-tail units into a…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a…
We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
In this thesis, the tail properties of multivariate Archimedean copulas are investigated using known representation theorems involving L1-norm symmetric distributions and the Williamson d-transform. Several new results on the asymptotic…
We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant…
Let $Y=\sum_{k\ge 1} 1_{A_k}$ be an infinite sum of the indicators of independent events. We investigate a precise (as opposed to logarithmic) first-order asymptotic behavior of the tail probabilities $\mathbb{P}\{Y\ge n\}$ and the point…
Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a…
Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…
In this paper the following result, which allows one to decouple U-Statistics in tail probability, is proved in full generality. Theorem 1. Let $X_i$ be a sequence of independent random variables taking values in a measure space $S$, and…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…