Related papers: Mixed Poisson families with real-valued mixing dis…
Based on the negative binomial model for the duration of wet periods measured in days, an asymptotic approximation is proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the…
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…
We present a novel reshuffling exchange model and investigate its long time behavior. In this model, two individuals are picked randomly, and their wealth $X_i$ and $X_j$ are redistributed by flipping a sequence of fair coins leading to a…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities…
We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an…
Fully describing the entire data set is essential in multivariate risk assessment, since moderate levels of one variable can influence another, potentially leading it to be extreme. Additionally, modelling both non-extreme and extreme…
Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this…
The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that…
Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however,…
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…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Interevent times in temporal contact data from humans and animals typically obey heavy-tailed distributions, and this property impacts contagion and other dynamical processes on networks. We theoretically show that distributions of…
The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…
We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating question has been whether a freely stable random matrix has…