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Application of spatial statistics in forestry
Jakůbková, Blanka ; Saxl, Ivan (referee) ; Pawlas, Zbyněk (advisor)
Presented thesis deals with the study of point processes and marked point processes, it considers their summary characteristics (both numerical and functional) and hypothesis tests for the purpose of application to real forestry data. The estimators of characteristics are summarized, in their construction edge e ects caused by bounded observation window has to be taken into account. A particular attention is devoted to the case when the data are formed by the realization of a stationary marked point process in several disjoint observation windows. The estimators of summary characteristics are de ned and for some of them their properties are compared based on the simulation study. In the statistical data analysis, it is assumed stationarity of a point process which describes two-dimensional arrangement of tree locations in a forest. Qualitative and quantitative attributes of individual trees are considered. Their mutual relationship is examined and the dependence on tree positions is assessed.
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Probabilistic Models and Methods for the Analysis of Sports Results
Rambousková, Daniela ; Saxl, Ivan (referee) ; Volf, Petr (advisor)
The statistical modelling on a sports field is in the process of a great development. Sports clubs have gradually changed into commercial companies and thus many possibilities how to take advantages of statistical instruments have emerged. Undoubtedly, the most popular task is the prediction of possible future results. The first part of this thesis summarizes the most interesting methods and types of solutions that were developed primarily for football matches. In this case the Poissons' regression models are mainly used. However, when the influences of time are taken into consideration, these models become more difficult and complicated for computations. The second part deals with the statistical survival analysis and random point processes and tries to find its utilization and connection with the predictions of the results of sports matches. On the basis of the Cox' regression model, a simple model for ice-hockey matches is derived here. This model estimates offensive and defensive forces of every team and other influences, for instance power plays and home environment. It describes the match as a random point process, where the time of scoring represents its random points. The model is applied on the data obtained from the first thirteen rounds of the Czech National Ice-hockey League and the received...
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Application of statitistics to the measurement of characteristics of planar objects
Šedivý, Ondřej ; Beneš, Viktor (referee) ; Saxl, Ivan (advisor)
Nazev prace: Aplikace gcometricke statistiky na mefeni charakteristik rovinnych objektu Autor: Ondfej Sedivy Katcdra: Katedra pravdcpodobnosli a matematicke statistiky Vcdouci bakalafske pracc: RNDr. Ivan Saxl, DrSc, c mail vedouciho: saxl@math.cas.cz Abstrakt: Ci'lem prace je podat strucny a co nejpristupneji napsany pfehled odhadu charakteristik rovinnych objektu z vyberu ponzenych geometrickyini prostfedky. Prvni dvc kapitoly jsou obecncjst'ho razu. Pojednavaji o rozdilech mczi klasickym a geometrickym vyberem z populace a naznafiujf n^ktere zakladni principy dale vyuiivane. Naslcduji ukazky pouziti geomelrickc statistiky k odhadum zakladnich charakteristik pro rovinne souboiy bodu, kfivek a ploch. Kratka zaverecna stat'je včnovana zpusobu zkoumani trojrozmernych objektO. V textu jsou take podrobne zpracovany historicke Buffonovy ulohy ojehle a ctverci. Klicuva slova: geometricka statistika, klasicky a gcomctricky vybeY, Buffonovy ulohy Title: Application of geometrical statistics for measuring characteristics of planar objects Author: Ondfej Sedivy Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ivan Saxl, DrSc. Supervisor's e-mail address: saxl@math.cas.cz Abstract: The aim of this work is to offer a short and clearly written review of estimations of characteristics...
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Mathematics in Paracelsus' time
Saxl, Ivan
The life of five mathematicians, Nicolas Choquet, Éstienne de la Roche, Johannes Widmann, Adam Ries and Albrecht Dürer, are described and their main mathematical achievements consisting in writing textbooks of different kind are discussed.
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