Název:
Charakteristiky druhého řádu bodových procesů
Překlad názvu:
Second-order characteristics of point processes
Autoři:
Gupta, Archit ; Pawlas, Zbyněk (vedoucí práce) ; Prokešová, Michaela (oponent) Typ dokumentu: Diplomové práce
Rok:
2019
Jazyk:
eng
Abstrakt: In this thesis we examine estimation of the K-function which is an important second-order characteristic in the theory of spatial point processes. Besides Ripley's K-function based on a spherical structuring element we also work with the multiparameter K-function where the struc- turing element is rectangular. We consider the Poisson point process model, which is the fundamental model for complete spatial randomness. We de- rive expressions for both bias and variance of the estimators. The primary goal of this thesis is the study of different edge correction methods that are available for the K-function. Using simulations we also study a few variance approximations proposed in the literature and compare them with empirical variances. 1