Second-order characteristics of point processes
Charakteristiky druhého řádu bodových procesů
diploma thesis (DEFENDED)

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http://hdl.handle.net/20.500.11956/107216Identifiers
Study Information System: 194647
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- Kvalifikační práce [10593]
Author
Advisor
Referee
Prokešová, Michaela
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, Mathematical Statistics and Econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
12. 6. 2019
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
English
Grade
Very good
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