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The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the…
We consider the superposition of symmetric simple exclusion dynamics speeded-up in time, with spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We show that the mixing time has an exponential lower bound in…
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference.…
Methods for unsupervised anomaly detection suffer from the fact that the data is unlabeled, making it difficult to assess the optimality of detection algorithms. Ensemble learning has shown exceptional results in classification and…
We consider $\psi$-mixing dynamical systems $(\mathcal{X},T,B,\mu)$ and we find conditions on families of sets $\{\mathcal{U}_n\subset \mathcal{X}:n\in\mathbb{N}\}$ so that $\mu(\mathcal{U}_n)\tau_n$ tends in law to an exponential random…
Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…
In this paper, an alternative count distribution suitable for modeling over dispersed, zero vertex unimodality and monotonically decreasing data sets. Though the proposed probability model includes Gauss Hypergeometric special function, it…
Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…
Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time…
In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull-Poisson (EWP) distribution. The new distribution arises on a latent…
Time-to-event models are a popular tool to analyse data where the outcome variable is the time to the occurrence of a specific event of interest. Here we focus on the analysis of time-to-event outcomes that are either intrisically discrete…
An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
Accounting for both rare events and complex sampling presents challenges when quantifying uncertainty for rate estimation in autonomous vehicle performance evaluation. In this paper, we introduce a statistical formulation of this problem…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold.…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
Anomaly detection plays an important role in modern data-driven security applications, such as detecting suspicious access to a socket from a process. In many cases, such events can be described as a collection of categorical values that…
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…