Related papers: Heavy-tailed phase-type distributions: A unified a…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…
We demonstrate that distributions of human response times have power-law tails and, among closed-form distributions, are best fit by the generalized inverse gamma distribution. We speculate that the task difficulty tracks the half-width of…
This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching…
We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…
Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
For multitype branching processes with immigration evolving in a random environment and producing a final product we find the tail distribution of the size of the final product accumulated in the system for a life period. Using this result…
We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…
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…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
Continuous-time multistate models are widely used for analyzing interval-censored data on disease progression over time. Sometimes, diseases manifest differently and what appears to be a coherent collection of symptoms is the expression of…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a…
We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with heavy tail of maximum distribution.
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
We consider continuous time risk processes in which the claim sizes are dependent and non-identically distributed phase-type distributions. The class of distributions we propose is easy to characterize and allows to incorporate the…
We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…