Search results for "K-function"
showing 9 items of 9 documents
Gas cell studies of thorium using filament dispensers at IGISOL
2020
Abstract Filament-based dispensers of thorium have been investigated at the IGISOL facility, Jyvaskyla, for potential use as a thorium ion source for future collinear laser spectroscopy experiments. Several different filaments were manufactured in the Institute of Atomic and Subatomic Physics of TU Wien, with 232Th and 229Th prepared on tantalum substrates either by drying thorium nitrate solution or via molecular plating, while adding a layer of zirconium for oxide reduction. The filaments were characterized in a helium-filled gas cell by performing selective and efficient in-gas-cell resonance laser ionization and by analyzing the resulting ion beams by mass spectrometry. Additionally, th…
Some properties of local weighted second-order statistics for spatio-temporal point processes
2019
Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data into residuals as a result of a thinning or a rescaling procedure. We alternatively consider here second-order statistics coming from weighted measures. Motivated by Adelfio and Schoenberg (Ann Inst Stat Math 61(4):929–948, 2009) for the temporal and spatial cases, we consider an extension to the spatio-temporal context in addition to focussing on local characteristics. In particular, our proposed method assesses goodness-of-fit of spatio-temporal models by using local weighted second-order statistics, computed after weighting the contribution of each observed point by the…
Local inhomogeneous weighted summary statistics for marked point processes
2023
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture different kinds of local dependence structures. We first derive some basic properties and show how these new statistical tools can be used to construct most existing summary statistics for (marked) point processes. We then propose a local test of random labelling. This procedure allows us to identify points, and consequently regions, where the random labelling assumption does not hold, e.g.~when the (functional) marks are spatially dependent. Through a simulatio…
Spatio-temporal cluster detection of chickenpox in Valencia, Spain in the period 2008-2012.
2015
Chickenpox is a highly contagious airborne disease caused by <em>Varicella zoster</em>, which affects nearly all non-immune children worldwide with an annual incidence estimated at 80-90 million cases. To analyze the spatiotemporal pattern of the chickenpox incidence in the city of Valencia, Spain two complementary statistical approaches were used. First, we evaluated the existence of clusters and spatio-temporal interaction; secondly, we used this information to find the locations of the spatio-temporal clusters via the space-time permutation model. The first method used detects any aggregation in our data but does not provide the spatial and temporal information. The second me…
The Evolution of Territorial Occupation:
2012
International audience; The analysis of territorial changes over time raises many methodological questions. Despite a very frequent use of spatial analysis methods, few works underline their methodological shortcomings. This paper considers a comparison and discussion of exploratory statistical methods (notably Ripley's K function and its derivatives). It is worth noting three parameters in archaeological spatial analysis: scale, quality and quantity of input data. Archaeological data are intrinsically heterogeneous. Therefore, our approach proposes a multiscalar process integrating heterogeneous data. We describe a range of methods for the description and analysis of heterogeneous spatial …
Local test of random labelling for functional marked point processes
2022
We introduce the local t-weighted marked nth-order inhomogeneous K-function, in a Functional Marked Point Processes framework. We employ the proposed summary statistics to run a local test of random labelling, useful to identify points, and consequently regions, where this assumption does not hold, i.e. the functional marks are spatially dependent.
Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators
2016
This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.
Clustering of spatial point patterns
2006
Spatial point patterns arise as the natural sampling information in many problems. An ophthalmologic problem gave rise to the problem of detecting clusters of point patterns. A set of human corneal endothelium images is given. Each image is described by using a point pattern, the cell centroids. The main problem is to find groups of images corresponding with groups of spatial point patterns. This is interesting from a descriptive point of view and for clinical purposes. A new image can be compared with prototypes of each group and finally evaluated by the physician. Usual descriptors of spatial point patterns such as the empty-space function, the nearest distribution function or Ripley's K-…
Weighted local second-order statistics for complex spatio-temporal point processes
2019
Spatial, temporal, and spatio-temporal point processes, and in particular Poisson processes, are stochastic processes that are largely used to describe and model the distribution of a wealth of real phenomena. When a model is fitted to a set of random points, observed in a given multidimensional space, diagnostic measures are necessary to assess the goodness-of-fit and to evaluate the ability of that model to describe the random point pattern behaviour. The main problem when dealing with residual analysis for point processes is to find a correct definition of residuals. Diagnostics of goodness-of-fit in the theory of point processes are often considered through the transformation of data in…