相关论文: Control Charts for Poisson Counts based on the Ste…

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…

We demonstrate that two approximations to the chi^2 statistic as popularly employed by observational astronomers for fitting Poisson-distributed data can give rise to intrinsically biased model parameter estimates, even in the high counts…

Random discrete distributions, say $F,$ known as species sampling models, represent a rich class of models for classification and clustering, in Bayesian statistics and machine learning. They also arise in various areas of probability and…

We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…

We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…

We use Stein's method to obtain distributional approximations of subgraph counts in the uniform attachment model or random directed acyclic graph; we provide also estimates of rates of convergence. In particular, we give uni- and…

This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…

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…

Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…

A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{\alpha, \beta}(\lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that…

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…

A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…

Because of the curse-of-dimensionality, high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution and complicated dependency…

In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…

In statistical process control, procedures are applied that require relatively strict conditions for their use. If such assumptions are violated, these methods become inefficient, leading to increased incidence of false signals. Therefore,…

We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…

A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example,…

In Statistical Process Control, control charts are often used to detect undesirable behavior of sequentially observed quality characteristics. Designing a control chart with desirably low False Alarm Rate (FAR) and detection delay ($ARL_1$)…