Related papers: Nearest-Neighbor and Contact Distance Distribution…
Project a collection of points on the high-dimensional sphere onto a random direction. If most of the points are sufficiently far from one another in an appropriate sense, the projection is locally close in distribution to the Poisson point…
In this letter, we characterize the distribution of the number of users associated with the typical base station (BS), termed the typical cell load, in a cellular network where the BSs are distributed as a homogeneous Poisson point process…
High-dimensional clustering often relies on geometric or local-similarity structure, but the dominant separation between groups may not always be location-based. Differences in dispersion can create asymmetric local-neighborhood patterns:…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…
Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…
We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our…
Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…
The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…
Nowadays, many machine learning procedures are available on the shelve and may be used easily to calibrate predictive models on supervised data. However, when the input data consists of more than one unknown cluster, and when different…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion…
We study the graph constructed on a Poisson point process in $d$ dimensions by connecting each point to the $k$ points nearest to it. This graph a.s. has an infinite cluster if $k > k_c(d)$ where $k_c(d)$, known as the critical value,…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its…
A worst case distribution is a minimiser of the expectation of some random payoff within a family of plausible risk factor distributions. The plausibility of a risk factor distribution is quantified by a convex integral functional. This…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…