### Skapa referens, olika format (klipp och klistra)

**Harvard**

Månsson, M. (1996) *On Clustering of Random Points in the Plane and in Space*. Göteborg : Chalmers University of Technology (Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, nr: 1178).

** BibTeX **

@book{

Månsson1996,

author={Månsson, Marianne},

title={On Clustering of Random Points in the Plane and in Space},

isbn={91-7197-290-0},

abstract={If n points are independently and uniformly distributed in a large rectangular parallelepiped, A in R<sup>d</sup>, d =2,3, they may possibly aggregate in such a way that they are contained in some translate of a given convex set C in A. If the points are replaced by copies of C, these translated sets may have a non-empty intersection. The probabilities of these two events are in fact equal. This thesis consists of three separate papers, of which parts of the first and the second are devoted to the derivation of this probability. Also generalizations are considered, which allow the sets to be unequal, and to be rotated according to a uniform distribution.<p /> In the latter part of the first paper the number of subsets consisting of k<n points which can be covered by some translate of C in A is considered in the plane. When n is large and C is small, this number is approximately Poisson, as shown by means of the Stein-Chen method. This approximation is used in some applications, for instance to find the limiting distribution of the maximal number of points which can be covered by some translate of C<sub>n</sub>, if the sets in {C<sub>n</sub>} decrease at a certain rate as n tends to infinity.<p /> To each k-subset, which can be covered by some translate of C, can be attached its position on A, and the smallest s in R<sup>+</sup> for which some translate of sC covers the k points. Poisson process approximation of three point processes determined by these positions and sizes are dealt with in the third paper.<p /> All approximations are considered also when the total number of points is not fixed but have a Poisson distribution, so that the points constitute a Poisson process.},

publisher={Institutionen för matematik, Chalmers tekniska högskola,},

place={Göteborg},

year={1996},

series={Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 1178},

keywords={geometric probability, integral geometry, convex sets, random intersections, mixed volumes, scan statistics, Poisson approximation, Stein-Chen method, convergence of point processes},

}

** RefWorks **

RT Dissertation/Thesis

SR Print

ID 1146

A1 Månsson, Marianne

T1 On Clustering of Random Points in the Plane and in Space

YR 1996

SN 91-7197-290-0

AB If n points are independently and uniformly distributed in a large rectangular parallelepiped, A in R<sup>d</sup>, d =2,3, they may possibly aggregate in such a way that they are contained in some translate of a given convex set C in A. If the points are replaced by copies of C, these translated sets may have a non-empty intersection. The probabilities of these two events are in fact equal. This thesis consists of three separate papers, of which parts of the first and the second are devoted to the derivation of this probability. Also generalizations are considered, which allow the sets to be unequal, and to be rotated according to a uniform distribution.<p /> In the latter part of the first paper the number of subsets consisting of k<n points which can be covered by some translate of C in A is considered in the plane. When n is large and C is small, this number is approximately Poisson, as shown by means of the Stein-Chen method. This approximation is used in some applications, for instance to find the limiting distribution of the maximal number of points which can be covered by some translate of C<sub>n</sub>, if the sets in {C<sub>n</sub>} decrease at a certain rate as n tends to infinity.<p /> To each k-subset, which can be covered by some translate of C, can be attached its position on A, and the smallest s in R<sup>+</sup> for which some translate of sC covers the k points. Poisson process approximation of three point processes determined by these positions and sizes are dealt with in the third paper.<p /> All approximations are considered also when the total number of points is not fixed but have a Poisson distribution, so that the points constitute a Poisson process.

PB Institutionen för matematik, Chalmers tekniska högskola,

T3 Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 1178

LA eng

OL 30