… , SGD exhibits a ‘heavy-tail phenomenon’, meaning that the law of the iterates converges to
a heavy-tailed distribution. We rigorously prove that, this phenomenon is not specific to deep …

… Just like the popular Hill estimator in the continuous heavy-tail situation, the estimator ̂β
we propose can be derived by means of a suitable reformulation of the regularly varying …

… claim size, the ruin probability is still decaying at an exponential speed. Chapter 3 further
handles approximations of the ruin probability: if one approximates the ruin probability by an …

… loss data, statistical investigation quite often indicates random variables with an heavy tail.
As described in the introductory part (Chapter 1) of the book, many events in the stock market …

… In contrast to the heavy tail setting, we do not establish results about unreliable estimation in
… that the estimation problem is harder for the heavy tail case (see the discussion in Section 3)…

… a versatile hydrologic probability model with three parameters. The proposed model is a …
From this, it is evident the distribution reflects light and heavy tail behavior. Moreover, it is …

… We show that some heavy-tail phenomena observed in large deviations can be explained
by the same mechanism as for the Wiener chaoses, meaning that the deviations are created, …

… This heavy tail behavior may surprise flood managers and … Despite its high importance, the
literature on the heavy tail behavior … the statistical conditions for the emergence of heavy tail …

… models" (GLM), a new class of heavytailed probability distributions, to describe real networks
than the strict scale-free property. In generalized Lomax models… and heavy-tail behavior) of …

… a heavy-tail rare … of heavy-tail inputs would lead to estimates as if the system is light-tail,
and the ultimate effect could be that the estimation error is as large as the rare-event probability …