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The asymptotic behaviour of a closed BCMP network, with $n$ queues and $m_n$ clients, is analyzed when $n$ and $m_n$ become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We…

Probability · Mathematics 2012-07-16 Guy Fayolle , Jean-Marc Lasgouttes

We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…

Statistics Theory · Mathematics 2026-05-06 Martin Bladt , Rasmus Frigaard Lemvig

We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

Probability · Mathematics 2024-04-11 Simone Baldassarri , Gianmarco Bet

This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general…

Risk Management · Quantitative Finance 2021-04-20 Sangita Das , Suchandan Kayal

This paper studies proportional risk sharing at claim occurrence time in community-based insurance. Each participant is modeled by an individual Cram\'er-Lundberg surplus process, and, whenever a claim is reported within the pool, its cost…

Probability · Mathematics 2026-04-01 Michel Denuit , José Miguel Flores-Contró , Christian Y. Robert

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for…

Methodology · Statistics 2026-01-12 Luis E. Nieto-Barajas , Rodrigo S. Targino

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…

Probability · Mathematics 2018-04-04 H. L. Gan , Eric D. Kolaczyk

We study the asymptotic distributions of the spiked eigenvalues and the largest nonspiked eigenvalue of the sample covariance matrix under a general covariance matrix model with divergent spiked eigenvalues, while the other eigenvalues are…

Statistics Theory · Mathematics 2017-11-07 Tony Cai , Xiao Han , Guangming Pan

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

Probability · Mathematics 2018-08-06 Günter Last , Franz Nestmann , Matthias Schulte

Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…

Probability · Mathematics 2011-04-11 Thomas G. Kurtz , Eliane R. Rodrigues

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The…

Probability · Mathematics 2008-12-18 Zhidong Bai , Jian-feng Yao

Modeling insurance claim amounts and classifying claims into different risk levels are critical yet challenging tasks. Traditional predictive models for insurance claims often overlook the valuable information embedded in claim…

Applications · Statistics 2024-10-08 Yanxi Hou , Xiaolan Xia , Guangyuan Gao

In this work, we consider an estimation method in sparse Poisson models inspired by [1] and provide novel sign consistency results under mild conditions.

Statistics Theory · Mathematics 2023-03-27 Marina Gomtsyan , Céline Lévy-Leduc , Sarah Ouadah , Laure Sansonnet

The paper considers multivariate discrete random sums with equal number of summands. Such distributions describe the total claim amount received by a company in a fixed time point. In Queuing theory they characterize cumulative waiting…

Probability · Mathematics 2016-12-12 Pavlina Jordanova

In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…

Methodology · Statistics 2016-10-05 Deepesh Bhati , Pooja Kumawat , E. Gómez Déniz

We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation. This enables us to apply general limit theorems for super-critical Crump-Mode-Jagers branching…

Probability · Mathematics 2022-10-04 Jean Bertoin

Consider a sample of size $N$ from a population governed by a hierarchical species sampling model. We study the large $N$ asymptotic behavior of the number ${\bf K}_N$ of clusters and the number ${\bf M}_{r,N}$ of clusters with frequency…

Probability · Mathematics 2025-01-17 Stefano Favaro , Shui Feng , J. E. Paguyo

Generalized Linear Mixed Models (GLMMs) are widely used for analysing clustered data. One well-established method of overcoming the integral in the marginal likelihood function for GLMMs is penalized quasi-likelihood (PQL) estimation,…

Statistics Theory · Mathematics 2024-05-03 Xu Ning , Francis Hui , Alan Welsh

In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…

Probability · Mathematics 2014-06-24 Alexandru V. Asimit , Enkelejd Hashorva , Dominik Kortschak

The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator…

Statistics Theory · Mathematics 2007-06-13 Chang Xuan Mao