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Inhomogeneous Poisson Process (inhomogeneous + poisson_process)

Distribution by Scientific Domains
Mathematics and Statistics80%

Selected Abstracts

Stochastic and Relaxation Processes in Argon by Measurements of Dynamic Breakdown Voltages

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7 2005
V. Lj.
Abstract Statistically based measurements of breakdown voltages Ub and breakdown delay times td and their variations in transient regimes of establishment and relaxation of discharges are a convenient method to study stochastic processes of electrical breakdown of gases, as well as relaxation kinetics in afterglow. In this paper the measurements and statistical analysis of the dynamic breakdown voltages Ub for linearly rising (ramp) pulses in argon at 1.33 mbar and the rates of voltage rise k up to 800 V s,1 are presented. It was found that electrical breakdowns by linearly rising (ramp) pulses is an inhomogeneous Poisson process caused by primary and secondary ionization coefficients , , , and electron yield Y variations on the voltage (time). The experimental breakdown voltage distributions were fitted by theoretical distributions by applying approximate analytical and numerical models. The afterglow kinetics in argon was studied based on the dependence of the initial electron yield on the relaxation time Y0 (, ) derived from fitting of distributions. The space charge decay was explained by the surface recombination of nitrogen atoms present as impurities. The afterglow kinetics and the surface recombination coefficients on the gas tube and cathode were determined from a gas-phase model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Modelling the process of incoming problem reports on released software products

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 2 2004
Geurt Jongbloed
Abstract For big software developing companies, it is important to know the amount of problems of a new software product that are expected to be reported in a period after the date of release, on a weekly basis. For each of a number of past releases, weekly data are present on the number of such reports. Based on the type of data that is present, we construct a stochastic model for the weekly number of problems to be reported. The (non-parametric) maximum likelihood estimator for the crucial model parameter, the intensity of an inhomogeneous Poisson process, is defined. Moreover, the expectation maximization algorithm is described, which can be used to compute this estimate. The method is illustrated using simulated data. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Cluster Pattern Detection in Spatial Data Based on Monte Carlo Inference

BIOMETRICAL JOURNAL, Issue 4 2007
Radu Stefan Stoica
Abstract Clusters in a data point field exhibit spatially specified regions in the observation window. The method proposed in this paper addresses the cluster detection problem from the perspective of detection of these spatial regions. These regions are supposed to be formed of overlapping random disks driven by a marked point process. The distribution of such a process has two components. The first is related to the location of the disks in the field of observation and is defined as an inhomogeneous Poisson process. The second one is related to the interaction between disks and is constructed by the superposition of an area-interaction and a pairwise interaction processes. The model is applied on spatial data coming from animal epidemiology. The proposed method tackles several aspects related to cluster pattern detection: heterogeneity of data, smoothing effects, statistical descriptors, probability of cluster presence, testing for the cluster presence. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data

BIOMETRICS, Issue 2 2010
Peter J. Diggle
Summary We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio-temporal point-process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum-likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial-likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain. [source]

The Beta-Binomial Model for Host Specificity among Organisms in Trophic Interactions

BIOMETRICS, Issue 3 2000
Ola H. Diserud
Summary. In this paper, we present a new stochastic model where the host specificity among organisms in trophic interactions in a community, say parasite-host interactions, is estimated by a beta-binomial model. The expected proportion of the host species in a community that a given parasite species is utilizing is modeled as a realization from an inhomogeneous Poisson process, where the rate of this process is assumed to be proportional to a beta probability distribution. The observed number of host species utilized by the parasites is then binomially distributed with the number of trials equaling the number of different host species in the sample. When the degree of polyphagy is estimated by the parameters of the beta-binomial model, quantities like community host specificity and the expected total number of parasite species that will utilize the host species in the community can be predicted as functions of the number of host species available. The predictions can then be applied in analysis of, e.g., symbiotic interactions among organisms, local species richness, and community structure. [source]