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Point processes on linear networks
Moravec, Jan ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
The central theme of this thesis is the theory of point processes on linear net- works, in particular two kinds of the network K-function. The first part is devoted to the theory of stationary point processes in the plane, including the K-function and its estimator. The second part is concerned with the theory of point proces- ses on linear networks. There is defined the Okabe-Yamada network K -function and its estimator, the geometrically corrected network K-function, including its estimator, and there are explained their theoretical properties. In the third part we examine the ability of these two kinds of the network K-function to detect clustering or regularity in point processes on linear networks. There is explained the envelope test, the refined envelope test and the deviation tests. The software environment R with library spatstat is used for simulations.
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Point processes on linear networks
Moravec, Jan ; Prokešová, Michaela (advisor) ; Pawlas, Zbyněk (referee)
The central theme of this thesis is the theory of point processes on linear net- works, in particular two kinds of the network K-function. The first part is devoted to the theory of stationary point processes in the plane, including the K-function and its estimator. The second part is concerned with the theory of point proces- ses on linear networks. There is defined the Okabe-Yamada network K -function and its estimator, the geometrically corrected network K-function, including its estimator, and there are explained their theoretical properties. In the third part we examine the ability of these two kinds of the network K-function to detect clustering or regularity in point processes on linear networks. There is explained the envelope test, the refined envelope test and the deviation tests. The software environment R with library spatstat is used for simulations.
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