Related papers: Inhomogeneous phase--type distributions and heavy …
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are…
Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…
The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed…
Assessing and managing risks in a changing climate requires projections that account for decision-relevant uncertainties. These deep uncertainties are often approximated by ensembles of Earth-system model runs that sample only a subset of…
We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the…
In this work we focus on modeling a little studied type of traffic, namely the network traffic generated from endhosts. We introduce a parsimonious parametric model of the marginal distribution for connection arrivals. We employ mixture…
The aim of this paper is to develop the theory of distributions, not necessarily of compact support, in a topos model of Synthetic Differential Geometry, the so-called "Cahiers Topos". As an application, we study the evolution through time…
Analysis of matrix-variate data is becoming increasingly common in the literature, particularly in the field of clustering and classification. It is well-known that real data, including real matrix-variate data, often exhibit high levels of…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for…
A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal…
Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma…
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…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…
We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding…
Motivated by seminal paper of Kozlov et al.(1975) we consider in this paper a branching process with a geometric offspring distribution parametrized by random success probability $A$ and immigration equals $1$ in each generation. In…