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We present long range statistical properties of a recently introduced unitary random matrix ensemble, whose short range correlations were found to describe a transition from Wigner to Poisson type as a function of a single parameter.
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…
This paper explores foundational and applied aspects of survival analysis, using fall risk assessment as a case study. It revisits key time-related probability distributions and statistical methods, including logistic regression, Poisson…
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate \lambda. We…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases,…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial…
Interevent times have been studied across various disciplines in search for correlations. In this paper we show analytical and numerical evidence that at the population level a power-law can be obtained by assuming poissonian agents with…
Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…